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1956-1
Yaschenko I. V. Make your dollar bigger now!!! Math. Intelligencer, 1998, 20(2), 38–40.
1956-1 — N. P. Dolbilin
Tarasov A. On Arnold's problem on a “folded rouble”, in preparation.
1958-1 — V. I. Arnold
Arnold V. I. Small denominators and problems of stability of motion in classical and celestial mechanics. Russian Math. Surveys, 1963, 18(6), 85–191.
Kontsevich M. L. Lyapunov exponents and Hodge theory. In: The Mathematical Beauty of Physics (Saclay, 1996). A memorial volume for Claude Itzykson. Editors: J. M. Drouffe and J. B. Zuber. River Edge, NJ: World Scientific, 1997, 318–322. (Adv. Ser. Math. Phys., 24.)
Zorich A. V. How do the leaves of a closed 1-form wind around a surface? In: Pseudoperiodic Topology. Editors: V. Arnold, M. Kontsevich and A. Zorich. Providence, RI: Amer. Math. Soc., 1999, 135–178. (AMS Transl., Ser. 2, 197; Adv. Math. Sci., 46.)
1958-1 — A. V. Zorich
Arnold V. I. Small denominators and problems of stability of motion in classical and celestial mechanics. Russian Math. Surveys, 1963, 18(6), 85–191.
Arnoux P. Thèse, Université de Reims, 1981.
Boshernitzan M. D., Carroll C. R. An extension of Lagrange's theorem to interval exchange transformations over quadratic fields. J. Anal. Math., 1997, 72, 21–44.
Forni G. Deviation of ergodic averages for area-preserving flows on surfaces of higher genus. Ann. Math., Ser. 2, 2002, 155(1), 1–103.
Katok A. Invariant measures of flows on orientable surfaces. Sov. Math. Dokl., 1973, 14, 1104–1108.
Katok A. B., SinaĬ Ya. G., Stepin A. M. Theory of dynamical systems and general transformation groups with invariant measure. In: Itogi Nauki i Tekhniki VINITI. Mathematical Analysis, Vol. 13. Moscow: VINITI, 1975, 129–262 (in Russian). [The English translation: J. Sov. Math., 1977, 7, 974–1065.]
Keane M. Interval exchange transformations. Math. Z., 1975, 141, 25–31.
Keane M. Non-ergodic interval exchange transformations. Israel J. Math., 1977, 26(2), 188–196.
Keynes H., Newton D. A “minimal,” non-uniquely ergodic interval exchange transformation. Math. Z, 1976, 148(2), 101–105.
Kontsevich M. L. Lyapunov exponents and Hodge theory. In: The Mathematical Beauty of Physics (Saclay, 1996). A memorial volume for Claude Itzykson. Editors: J. M. Drouffe and J. B. Zuber. River Edge, NJ: World Scientific, 1997, 318–322. (Adv. Ser. Math. Phys., 24.)
Kontsevich M. L., Zorich A. V. Connected components of the moduli spaces of Abelian differentials with prescribed singularities. [Internet: http://www.arXiv.org/abs/math.GT/0201292]
Masur H. Interval exchange transformations and measured foliations. Ann. Math., Ser. 2, 1982, 115(1), 169–200.
Nogueira A. Almost all interval exchange transformations with flips are nonergodic. Ergod. Theory Dynam. Systems, 1989, 9(3), 515–525.
Nogueira A., Rudolph D. Topological weak-mixing of interval exchange maps. Ergod. Theory Dynam. Systems, 1997, 17(5), 1183–1209.
Oseledets V. I. The spectrum of ergodic automorphisms. Sov. Math. Dokl., 1966, 7, 776–779.
Rauzy G. Échanges d'intervalles et transformations induites. Acta Arithm., 1979, 34(4), 315–328.
Sataev E. A. On the number of invariant measures for flows on orientable surfaces. Math. USSR, Izv., 1975, 9, 813–830.
SinaĬ Ya. G., Khanin K. M. Mixing for some classes of special flows over rotations of the circle. Funct. Anal. Appl., 1992, 26(3), 155–169.
Veech W. A. Strict ergodicity in zero dimensional dynamical systems and the Kronecker-Weyl theorem mod 2. Trans. Amer. Math. Soc., 1969, 140, 1–33.
Veech W. A. Interval exchange transformations. J. Anal. Math., 1978, 33, 222–272.
Veech W. A. Gauss measures for transformations on the space of interval exchange maps. Ann. Math., Ser. 2, 1982, 115(1), 201–242.
Zorich A. V. Deviation for interval exchange transformations. Ergod. Theory Dynam. Systems, 1997, 17(6), 1477–1499.
Zorich A. V. How do the leaves of a closed 1-form wind around a surface? In: Pseudoperiodic Topology. Editors: V. Arnold, M. Kontsevich and A. Zorich. Providence, RI: Amer. Math. Soc., 1999, 135–178. (AMS Transl., Ser. 2, 197; Adv. Math. Sci., 46.)
1958-2 — S. A. Bogatyĭ
Altschiller-Court N. Modern Pure Solid Geometry. New York: Chelsea, 1964.
BogatyĬ S. A. Equihedral Tetrahedra. Moscow: Moscow Center for Continuous Mathematical Education Press, to appear.
Bogataya S. I., BogatyĬ S. A., Frolkina O. D. Affinity of volume-preserving mappings. Moscow Univ. Math. Bull., 2001, 56(6), 8–13.
Couderc P., Ballicioni A. Premier livre du tétraèdre. Paris: Gauthier-Villars, 1953.
DubrovskiĬ V. N. One more definition of an equihedral tetrahedron? Kvant, 1983, № 7,51, 63 (in Russian).
Kalinin A. Yu., Tereshin D. A. Stereometry-11. Moscow: Moscow Institute of Physics and Technology Press, 2001 (in Russian).
Kupitz Y. S., Martini H. The Fermat-Torricelli point and isosceles tetrahedra. J. Geometry, 1994, 49(1–2), 150–162.
Lenz H. Über einen Satz von June Lester zur Charakterisierung euklidischer Bewegungen. J. Geometry, 1987, 28(2), 197–201.
Lester J. A. Martin's theorem for Euclidean n-space and a generalization to the perimeter case. J. Geometry, 1986, 27(1), 29–35.
Matizen V. E. Equihedral and skeleton tetrahedra. Kvant, 1983, № 7, 34–38; Appendix to Kvant, 1995, № 1, 74–81 (in Russian).
Ovchinnikov S., Sharygin I. F. Nonstandard problems in stereometry. Kvant, 1979, № 6, 33–38, 58 (in Russian).
Prasolov V. V., Sharygin I. F. Problems in Stereometry. Moscow: Nauka, 1989 (in Russian).
Prasolov V. V., Tikhomirov V. M. Geometry. Moscow: Moscow Center for Continuous Mathematical Education Press, 1997 (in Russian).
Problem M9. Kvant, 1970, № 10, 42–44 (in Russian).
Sharygin I. F. Adding on a tetrahedron. Kvant, 1976, № 1, 61–64 (in Russian).
Sharygin I. F. Problem M353. Kvant, 1976, № 7, 31–32 (in Russian).
Vasil'ev N. B. Problem M319. Kvant, 1975, № 12, 39–41 (in Russian).
1958-2 — S. M. Gusein-Zade
Problem Book in Analytic Geometry and Linear Algebra. Editor: Yu. M. Smirnov Moscow: Physical and Mathematical Literature Publ., 2000 (in Russian).
1958-2 — M. L. Kontsevich
Shen' A. Entrance examinations to the Mekh-mat. Math. Intelligencer, 1994, 16(4), 6–10.
Vardi I. Mekh-mat entrance examinations problems. Preprint, Institut des Hautes Études Scientifiques, M/00/06. [Internet: http://www.ihes.fr/PREPRINTS/M00/M00-06.ps.gz]
1958-3 — S. Yu. Yakovenko
Arnold V. I. Dynamics of complexity of intersections. Bol. Soc. Brasil. Mat. (N.S.), 1990, 21(1), 1–10. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 489–499.]
Arnold V. I. Dynamics of intersections. In: Analysis, et cetera. Research papers published in honor of Jürgen Moser's 60th birthday. Editors: P. H. Rabinowitz and E. Zehnder. Boston, MA: Academic Press, 1990, 77–84.
Arnold V. I. Bounds for Milnor numbers of intersections in holomorphic dynamical systems. In: Topological Methods in Modern Mathematics. Proceedings of the symposium in honor of John Milnor's sixtieth birthday (Stony Brook, NY, 1991). Editors: L. R. Goldberg and A. V. Phillips. Houston, TX: Publish or Perish, 1993, 379–390.
Novikov D. I., Yakovenko S. Yu. Meandering of trajectories of polynomial vector fields in the affine n-space. Publ. Mat., 1997, 41(1), 223–242.
NovikovD. I, Yakovenko S. Yu. Trajectories of polynomial vector fields and ascending chains of polynomial ideals. Ann. Inst. Fourier (Grenoble), 1999, 49(2), 563–609.
1963-1
Arnold V. I. Small denominators and problems of stability of motion in classical and celestial mechanics. Uspekhi Mat. Nauk, 1963, 18(6), 91–192 (in Russian). [The English translation: Russian Math. Surveys, 1963, 18(6), 85–191.]
1963-1 — V. I. Arnold
Mather J. Arnold diffusion I: Announcement of the results. Preprint, Princeton University, November 25, 2002, 20 pp.
1963-1 — M. B. Sevryuk
Arnold V. I. On the instability of dynamical systems with many degrees of freedom. Sov. Math. Dokl., 1964, 5(3), 581–585. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 61–67.]
Arnold V. I., Avez A. Ergodic Problems of Classical Mechanics, 2nd edition. Redwood City, CA: Addison-Wesley, 1989. [The French original 1967.] [The first English edition 1968.]
Bernard P. Perturbation d'un hamiltonien partiellement hyperbolique. C. R. Acad. Sci. Paris, Sér. I Math., 1996, 323(2), 189–194.
Berti M. Some remarks on a variational approach to Arnold's diffusion. Discrete Contin. Dynam. Systems, 1996, 2(3), 307–314.
Berti M., Bolle P. Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei, Ser. 9, Mat. Appl, 2000, 11(4), 235–243.
Berti M., Bolle P. Fast Arnold diffusion in systems with three time scales. Discrete Contin. Dynam. Systems, 2002, 8(3), 795–811.
Berti M., Bolle P. A functional analysis approach to Arnold diffusion. Ann. Institut Henri Poincaré, Analyse non linéaire, 2002, 19(4), 395–450.
Bessi U. An approach to Arnold's diffusion through the calculus of variations. Nonlinear Anal. Theory Methods Appl., 1996, 26(6), 1115–1135.
Bessi U. Arnold's diffusion with two resonances. J. Differ. Equations, 1997, 137(2), 211–239.
Bessi U. Arnold's example with three rotators. Nonlinearity, 1997, 10(3), 763–781.
Bessi U., Chierchia L., Valdinoci E. Upper bounds on Arnold diffusion times via Mather theory. J. Math. Pures Appl., Sér. 9, 2001, 80(1), 105–129.
Bolotin S. V., Treshchëv D. V. Unbounded growth of energy in nonautonomous Hamiltonian systems. Nonlinearity, 1999, 12(2), 365–388.
Chierchia L. On the stability problem for nearly-integrable Hamiltonian systems. In: Seminar on Dynamical Systems (St. Petersburg, 1991). Editors: S. B. Kuksin, V. F. Lazutkin and J. Pöschel. Basel: Birkhäuser, 1994, 35–46.
Chierchia L. Arnold instability for nearly-integrable analytic Hamiltonian systems. In: Variational and Local Methods in the Study of Hamiltonian Systems (Trieste, 1994). Editors: A. Ambrosetti and G. F. Dell'Antonio. River Edge, NJ: World Scientific, 1995, 17–33.
Chierchia L. Non-degenerate ‘Arnold diffusion'. Preprint, archived in mp_arc@math.utexas.edu#96-137.
Chierchia L., Gallavotti G. Drift and diffusion in phase space. Ann. Institut Henri Poincaré, Physique théorique, 1994, 60(1), 1–144; erratum: 1998, 68(1), 135.
Chierchia L., Valdinoci E. A note on the construction of Hamiltonian trajectories along heteroclinic chains. Forum Math., 2000, 12(2), 247–255.
Chirikov B. V. Research in the theory of nonlinear resonance and stochasticity. Preprint of the Novosibirsk Institute for Nuclear Physics, the USSR Academy of Sciences, 1969, №267 (in Russian). [The English translation: CERN Transl., 1971, № 71–40.]
Chirikov B. V. A universal instability of many-dimensional oscillator systems. Phys. Rep., 1979, 52(5), 263–379.
Chirikov B. V., Ford J, Vivaldi F. Some numerical studies of Arnold diffusion in a simple model. In: Nonlinear Dynamics and the Beam-Beam Interaction (New York, 1979). Editors: M. Month and J. C. Herrera. New York: American Institute of Physics, 1980, 323–340. (AIP Conference Proceedings, 57.)
Chirikov B. V., Vecheslavov V. V. KAM integrability. In: Analysis, et cetera. Research papers published in honor of Jürgen Moser's 60th birthday. Editors: P. H. Rabinowitz and E. Zehnder. Boston, MA: Academic Press, 1990, 219–236.
Chirikov B. V., Vecheslavov V. V. Arnold diffusion in large systems. Zh. Eksp. Teor. Fiz., 1997, 112(3), 1132–1146.
Cresson J. A λ-lemma for partially hyperbolic tori and the obstruction property. Lett. Math. Phys., 1997, 42(4), 363–377.
Cresson J. Temps d'instabilité des systèmes hamiltoniens initialement hyperboliques. C. R. Acad. Sci. Paris, Sér I Math., 2001, 332(9), 831–834.
Cresson J. The transfer lemma for Graff tori and Arnold diffusion time. Discrete Contin. Dynam. Systems, 2001, 7(4), 787–800.
Delshams A., de la Llave R., Seara T. M. A geometric approach to the existence of orbits with unbounded energy in generic periodic perturbations by a potential of generic geodesic flows of \(\mathbb{T}^2 \). Commun. Math. Phys., 2000, 209(2), 353–392.
Diacu F. N. Featured Review 97h:70014. Math. Reviews, 1997.
Douady R. Stabilité ou instabilité des points fixes elliptiques. Ann. Sci. École Norm. Sup., Sér. 4, 1988, 21(1), 1–46.
Efthymiopoulos Ch., Voglis N., Contopoulos G. Diffusion and transient spectra in a 4-dimensional symplectic mapping. In: Analysis and Modelling of Discrete Dynamical Systems (Aussois, 1996). Editors: D. Benest and C. Froeschlé. Amsterdam: Gordon and Breach Sci. Publ., 1998, 91–106. (Advances Discrete Math. Appl., 1.)
Fontich E., Martín P. Construction of some unstable symplectic maps. In: Proceedings of the 2nd Catalan Days on Applied Mathematics (Odeillo, 1995). Editors: M. Sofonea and J.-N. Corvellec. Perpignan: Presses Univ. Perpignan, 1995, 95–103.
Fontich E., Martín P. Arnold diffusion in perturbations of analytic exact symplectic maps. Nonlinear Anal., 2000, 42(8), 1397–1412.
Fontich E., Martín P. Differentiable invariant manifolds for partially hyperbolic tori and a lambda lemma. Nonlinearity, 2000, 13(5), 1561–1593.
Fontich E., Martín P. Arnold diffusion in perturbations of analytic integrable Hamiltonian systems. Discrete Contin. Dynam. Systems, 2001, 7(1), 61–84.
Gadiyak G. V., Izrailev F. M., Chirikov B. V. Numerical experiments on the universal instability in nonlinear oscillator systems (Arnold diffusion). In: Proceedings of the 7th Intern. Conf. on Nonlinear Oscillations (Berlin, 1975); 1977, Vol. II, 1, 315 (in Russian).
Gallavotti G. Arnold's diffusion in isochronous systems. Math. Phys. Anal. Geom., 1999, 1(4), 295–312.
Gallavotti G. Hamilton-Jacobi's equation and Arnold's diffusion near invariant tori in a priori unstable isochronous systems. Rend. Semin. Mat. Univ. Politec. Torino, 1999, 55(4), 291–302.
Gallavotti G., Gentile G., Mastropietro V. Hamilton-Jacobi equation, heteroclinic chains and Arnold diffusion in three time scale systems. Nonlinearity, 2000, 13(2), 323–340.
Gallavotti G., Gentile G., Mastropietro V. On homoclinic splitting problems. Physica D, 2000, 137(1–2), 202–204.
Haller G. Diffusion at intersecting resonances in Hamiltonian systems. Phys. Lett. A, 1995, 200(1), 34–42.
Haller G. Fast diffusion and universality near intersecting resonances. In: Hamiltonian Systems with Three or More Degrees of Freedom (S'Agaró, 1995). Editor: C. Simó. Dordrecht: Kluwer Acad. Publ., 1999, 391–397. (NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 533.)
Holmes P. J., Marsden J. E. Mel'nikov's method and Arnold diffusion for perturbations of integrable Hamiltonian systems. J. Math. Phys., 1982, 23(4), 669–675.
Holmes P. J., Marsden J. E. Horseshoes and Arnold diffusion for Hamiltonian systems on Lie groups. Indiana Univ. Math. J., 1983, 32(2), 273–309.
Izrailev F. M., Chirikov B. V. Stochasticity of the simplest dynamical model with divided phase space. Preprint of the Novosibirsk Institute for Nuclear Physics, the USSR Academy of Sciences, 1968, № 191 (in Russian).
Kozlov V. V., Moshchevitin N. G. On diffusion in Hamiltonian systems. Moscow Univ. Mech. Bull., 1997, 52(5), 18–22.
Kozlov V. V., Moshchevitin N. G. Diffusion in Hamiltonian systems. Chaos, 1998, 8(1), 245–247.
Liao X., Saari D. G., Xia Zh. Instability and diffusion in the elliptic restricted three-body problem. Celest. Mech. Dynam. Astronom., 1998, 70(1), 23–39.
Lichtenberg A. J., Lieberman M. A. Regular and Chaotic Dynamics, 2nd edition. New York: Springer, 1992.
Lieberman M. A. Arnold diffusion in Hamiltonian systems with three degrees of freedom. In: Nonlinear Dynamics (New York, 1979). Editor: R. H. G. Helleman. New York: New York Acad. Sci., 1980, 119–142. (Annals New York Acad. Sci., 357.)
Lochak P. Effective speed of Arnold's diffusion and small denominators. Phys. Lett. A, 1990, 143(1–2), 39–42.
Lochak P. Canonical perturbation theory via simultaneous approximation. Russian Math. Surveys, 1992, 47(6), 57–133.
Lochak P. Arnold diffusion; a compendium of remarks and questions. In: Hamiltonian Systems with Three or More Degrees of Freedom (S'Agaró, 1995). Editor: C. Simó. Dordrecht: Kluwer Acad. Publ., 1999, 168–183. (NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 533.)
Lochak P. Supplement to “Arnold diffusion: a compendium of remarks and questions.” Preprint, archived in mp_arc@math.utexas.edu#98-293.
MacKay R. S. Transition to chaos for area-preserving maps. In: Nonlinear Dynamics Aspects of Particle Accelerators. Editors: J. M. Jowett, M. Month and S. Turner. Berlin: Springer, 1986, 390–454. (Lecture Notes in Phys., 247.)
MacKay R. S., Meiss J. D., Percival I. C. Transport in Hamiltonian systems. Physica D, 1984, 13(1–2), 55–81.
Marco J.-P. Transition le long des chaînes de tores invariants pour les systèmes hamiltoniens analytiques. Ann. Institut Henri Poincaré, Physique théorique, 1996, 64(2), 205–252.
Marco J.-P. Dynamics in the vicinity of double resonances. In: Proceedings of the IV Catalan Days of Applied Mathematics (Tarragona, 1998). Editors: C. García, C. Olivé and M. Sanromà. Tarragona: Univ. Rovira Virgili, 1998, 123–137.
Marco J.-P. Transition orbits and transition times along chains of hyperbolic tori. In: Hamiltonian Systems with Three or More Degrees of Freedom (S'Agaró, 1995). Editor: C. Simó. Dordrecht: Kluwer Acad. Publ., 1999, 480–484. (NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 533.)
Mastropietro V. Arnold diffusion and the d'Alembert precession problem. Reg. Chaot. Dynamics, 2001, 6(4), 355–375.
Moeckel R. Transition tori in the five-body problem. J. Differ. Equations, 1996, 129(2), 290–314.
Morbidelli A. Chaotic diffusion in celestial mechanics. Reg. Chaot. Dynamics, 2001, 6(4), 339–353.
Nekhoroshev N. N. An exponential estimate of the stability time for Hamiltonian systems close to integrable ones, I. Russian Math. Surveys, 1977, 32(6), 1–65.
Percival I. C. Chaos in Hamiltonian systems. Proc. Roy. Soc. London, Ser. A, 1987, 413(1844), 131–143.
Perfetti P. Fixed point theorems in the Arnold model about instability of the action-variables in phase-space. Discrete Contin. Dynam. Systems, 1998, 4(2), 379–391.
Pumariño A., Valls C. Three time scales systems exhibiting persistent Arnold's diffusion. Preprint, archived in mp_arc@math.utexas.edu#99-311.
Rudnev M., Wiggins S. On the use of the Mel'nikov integral in the Arnold diffusion problem. Preprint, archived in mp_arc@math.utexas.edu#97-494.
Rudnev M., Wiggins S. Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems. Physica D, 1998, 114(1–2), 3–80; erratum: 2000, 145(3–4), 349–354.
Rudnev M., Wiggins S. On a partially hyperbolic KAM theorem. Reg. Chaot. Dynamics, 1999, 4(4), 39–58.
Rudnev M., Wiggins S. On a homoclinic splitting problem. Reg. Chaot. Dynamics, 2000, 5(2), 227–242.
Sevryuk M. B. Featured Review 95b:58056. Math. Reviews, 1995.
Simó C, Valls C. A formal approximation of the splitting of separatrices in the classical Arnold's example of diffusion with two equal parameters. Nonlinearity, 2001, 14(6), 1707–1760.
Tennyson J. L., Lieberman M. A., Lichtenberg A. J. Diffusion in near-integrable Hamiltonian systems with three degrees of freedom. In: Nonlinear Dynamics and the Beam-Beam Interaction (New York, 1979). Editors: M. Month and J. C. Herrera. New York: American Institute of Physics Press, 1980, 272–301. (AIP Conference Proceedings, 57.)
Valdinoci E. Families of whiskered tori for a-priori stable/unstable Hamiltonian systems and construction of unstable orbits. Math. Phys. Electron. J., 2000, 6, Paper 2, 30pp. (electronic).
Vivaldi F. Weak instabilities in many-dimensional Hamiltonian systems. Rev. Modern Phys., 1984, 56(4), 737–754.
Wood B. P., Lichtenberg A. J., Lieberman M. A. Arnold and Arnold-like diffusion in many dimensions. Physica D, 1994, 71(1–2), 132–145.
Xia Zh. Arnold diffusion in the elliptic restricted three-body problem. J. Dyn. Differ. Equations, 1993, 5(2), 219–240.
Xia Zh. Arnold diffusion and oscillatory solutions in the planar three-body problem. J. Differ. Equations, 1994, 110(2), 289–321.
Xia Zh. Arnold diffusion with degeneracies in Hamiltonian systems. In: Dynamical Systems and Chaos (Hachioji, 1994), Vol. 1: Mathematics, Engineering and Economics. Editors: N. Aoki, K. Shiraiwa and Y. Takahashi. River Edge, NJ: World Scientific, 1995, 278–285.
Xia Zh. Arnold diffusion: a variational construction. In: Proceedings of the International Congress of Mathematicians, Vol.11 (Berlin, 1998). Doc. Math., 1998, Extra Vol. II, 867–877 (electronic).
ZaslavskiĬ G. M. Stochasticity of Dynamical Systems. Moscow: Nauka, 1984 (in Russian).
ZaslavskiĬ G. M., Chirikov B. V. Stochastic instability of nonlinear oscillations. Uspekhi Fiz. Nauk, 1971, 105(1), 3–39 (in Russian, for the English translation see Physics-Uspekhi).
ZaslavskiĬ G. M., Sagdeev R. Z., Usikov D. A., Chernikov A. A. Minimal chaos, stochastic web, and structures with symmetry of “quasicrystal” type. Uspekhi Fiz. Nauk, 1988, 156(2), 193–251 (in Russian, for the English translation see Physics-Uspekhi).
ZaslavskiĬ G. M., Sagdeev R. Z., Usikov D. A., Chernikov A. A. Weak Chaos and Quasi-regular Patterns. Cambridge: Cambridge University Press, 1991. (Cambridge Nonlinear Sci. Ser., 1.) [The Russian original 1991.]
ZaslavskiĬ G. M., Zakharov M. Yu., NeĬshtadt A. I., Sagdeev R. Z., Usikov D. A., Chernikov A. A. Multidimensional Hamiltonian chaos. Zh. Eksp. Teor. Fiz., 1989, 96(5), 1563–1586 (in Russian).
1963-2
Arnold V. I. Small denominators and problems of stability of motion in classical and celestial mechanics. Uspekhi Mat. Nauk, 1963, 18(6), 91–192 (in Russian). [The English translation: Russian Math. Surveys, 1963, 18(6), 85–191.]
1963-2 — M. B. Sevryuk
Birkhoff G. D. Dynamical Systems, 2nd edition. Providence, RI: Amer. Math. Soc., 1966. (Amer. Math. Soc. Colloquium Publ., 9.) [The first edition 1927.]
Chenciner A. La dynamique au voisinage d'un point fixe elliptique conservatif: de Poincaré et Birkhoff à Aubry et Mather. In: Séminaire Bourbaki, 1983–84, 622; Astérisque, 1985, 121–122, 147–170.
Genecand C. Transversal homoclinic orbits near elliptic fixed points of area-preserving diffeomorphisms of the plane. In: Dynamics Reported. Expositions in Dynamical Systems, Vol. 2. Editors: C. K. R. T. Jones, U. Kirchgraber and H.-O. Walther. Berlin: Springer, 1993, 1–30. (Dynam. Report.: Expos. Dynam. Syst., N. S., 2.)
Moser J. Nonexistence of integrals for canonical systems of differential equations. Commun. Pure Appl. Math., 1955, 8(3), 409–436.
Moser J. Stable and Random Motions in Dynamical Systems, with Special Emphasis on Celestial Mechanics. Princeton, NJ: Princeton University Press, 1973. (Ann. Math. Studies, 77.)
Zehnder E. Homoclinic points near elliptic fixed points. Commun. Pure Appl. Math., 1973, 26(2), 131–182.
1963-3
Arnold V. I. Small denominators and problems of stability of motion in classical and celestial mechanics. Uspekhi Mat. Nauk, 1963, 18(6), 91–192 (in Russian). [The English translation: Russian Math. Surveys, 1963, 18(6), 85–191.]
1963-3 — M. B. Sevryuk
Abad J. J., Koch H. Renormalization and periodic orbits for Hamiltonian flows. Commun. Math. Phys., 2000, 212(2), 371–394.
Abad J. J., Koch H., Wittwer P. A renormalization group for Hamiltonians: numerical results. Nonlinearity, 1998, 11(5), 1185–1194.
Arnold V. I. On the classical perturbation theory and the problem of stability of planetary systems. Sov. Math. Dokl., 1962, 3(4), 1008–1012. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 39–45.]
Arnold V. I. Small denominators and problems of stability of motion in classical and celestial mechanics. Russian Math. Surveys, 1963, 18(6), 85–191.
Berretti A., Gentile G. Scaling properties for the radius of convergence of a Lindstedt series: the standard map. J. Math. Pures Appl., Sér. 9, 1999, 78(2), 159–176.
Berretti A., Gentile G. Scaling properties for the radius of convergence of Lindstedt series: generalized standard maps. J. Math. Pures Appl., Sér. 9, 2000, 79(7), 691–713.
Berretti A., Gentile G. Bryuno function and the standard map. Commun. Math. Phys., 2001, 220(3), 623–656.
Bonetto F., Gentile G. On a conjecture for the critical behaviour of KAM tori. Math. Phys. Electron. J., 1999, 5, Paper 4, 8 pp. (electronic).
Broer H. W., Dumortier F., van Strien S. J., Takens F. Structures in Dynamics (Finite Dimensional Deterministic Studies). Amsterdam: North-Holland, Elsevier, 1991. (Studies Math. Phys., 2.)
Broer H. W., Huitema G. B., Sevryuk M. B. Quasi-Periodic Motions in Families of Dynamical Systems: Order amidst Chaos. Berlin: Springer, 1996. (Lecture Notes in Math., 1645.)
Celletti A. Rigorous and numerical determination of rotational invariant curves for the standard map. In: Analysis and Modelling of Discrete Dynamical Systems (Aussois, 1996). Editors: D. Benest and C. Froeschlé. Amsterdam: Gordon and Breach Sci. Publ., 1998, 149–180. (Advances Discrete Math. Appl., 1.)
Celletti A., Chierchia L. Rigorous estimates for a computer-assisted KAM theory. J. Math. Phys., 1987, 28(9), 2078–2086.
Celletti A., Chierchia L. Construction of analytic KAM surfaces and effective stability bounds. Commun. Math. Phys., 1988, 118(1), 119–161.
Celletti A., Chierchia L. A constructive theory of Lagrangian tori and computer-assisted applications. In: Dynamics Reported. Expositions in Dynamical Systems, Vol. 4. Editors: C. K. R. T. Jones, U. Kirchgraber and H.-O. Walther. Berlin: Springer, 1995, 60–129. (Dynam. Report.: Expos. Dynam. Syst., N. S., 4.)
Celletti A., Chierchia L. KAM stability estimates in Celestial Mechanics. Planetary Space Sci., 1998, 46(11–12), 1433–1440.
Celletti A., Falcolini C., Porzio A. Rigorous KAM stability statements for nonautonomous one-dimensional Hamiltonian systems. Rend. Semin. Mat. Univ. Politec. Torino, 1987, 45(1), 43–70.
Celletti A., Falcolini C., Porzio A. Rigorous numerical stability estimates for the existence of KAM tori in a forced pendulum. Ann. Institut Henri Poincaré, Physique théorique, 1987, 47(1), 85–111.
Celletti A., Froeschlé C. On the determination of the stochasticity threshold of invariant curves. Intern. J. Bifurcation and Chaos, 1995, 5(6), 1713–1719.
Celletti A., Giorgilli A., Locatelli U. Improved estimates on the existence of invariant tori for Hamiltonian systems. Nonlinearity, 2000, 13(2), 397–412.
Chandre C., Govin M., Jauslin H. R. Kolmogorov-Arnold-Moser renormalization-group approach to the breakup of invariant tori in Hamiltonian systems. Phys. Rev. E, Ser. 3, 1998, 57(2), part A, 1536–1543.
Chandre C., Govin M., Jauslin H. R., Koch H. Universality for the breakup of invariant tori in Hamiltonian flows. Phys. Rev. E, Ser. 3, 1998, 57(6), 6612–6617.
Chandre C., Laskar J., Benfatto G., Jauslin H. R. Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems. Physica D, 2001, 154(3–4), 159–170.
Chenciner A. La dynamique au voisinage d'un point fixe elliptique conservatif: de Poincaré et Birkhoff à Aubry et Mather. In: Séminaire Bourbaki, 1983–84, 622; Astérisque, 1985, 121–122, 147–170.
Gallavotti G., Gentile G., Mastropietro V. Field theory and KAM tori. Math. Phys. Electron. J., 1995, 1, Paper 5, 13 pp. (electronic).
Gentile G., Mastropietro V. A possible mechanism for the KAM tori breakdown. In: Hamiltonian Systems with Three or More Degrees of Freedom (S'Agaró, 1995). Editor: C. Simó. Dordrecht: Kluwer Acad. Publ., 1999, 372–376. (NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 533.)
Greene J. M. A method for determining a stochastic transition. J. Math. Phys., 1979, 20(6), 1183–1201.
Koch H. A renormalization group for Hamiltonians, with applications to KAM tori. Ergod. Theory Dynam. Systems, 1999, 19(2), 475–521.
Koch H. On the renormalization of Hamiltonian flows, and critical invariant tori. Discrete Contin. Dynam. Systems, 2002, 8(3), 633–646.
Locatelli U., Froeschlé C., Lega E., Morbidelli A. On the relationship between the Bruno function and the breakdown of invariant tori. Physica D, 2000, 139(1–2), 48–71.
MacKay R. S. Transition to chaos for area-preserving maps. In: Nonlinear Dynamics Aspects of Particle Accelerators. Editors: J. M. Jowett, M. Month and S. Turner. Berlin: Springer, 1986, 390–454. (Lecture Notes in Phys., 247.)
MacKay R. S. Renormalisation in Area-Preserving Maps. River Edge, NJ: World Scientific, 1993.
MacKay R. S., Meiss J. D., Percival I. C. Transport in Hamiltonian systems. Physica D, 1984, 13(1–2), 55–81.
MacKay R. S., Percival I. C. Converse KAM: theory and practice. Commun. Math. Phys., 1985, 98(4), 469–512.
Markus L., Meyer K. R. Generic Hamiltonian dynamical systems are neither integrable nor ergodic. Mem. Amer. Math. Soc., 1974, 144, 1–52.
Mather J. N., Forni G. Action minimizing orbits in Hamiltonian systems. In: Transition to Chaos in Classical and Quantum Mechanics. Editor: S. Graffi. Berlin: Springer, 1994, 92–186. (Lecture Notes in Math., 1589.)
Meiss J. D. Symplectic maps, variational principles, and transport. Rev. Modern Phys., 1992, 64(3), 795–848.
Olvera A., Simó C. An obstruction method for the destruction of invariant curves. Physica D, 1987, 26(1–3), 181–192.
Percival I. C. Chaos in Hamiltonian systems. Proc. Roy. Soc. London, Ser. A, 1987, 413(1844), 131–143.
Pöschel J. On small divisors with spatial structure. Habilitationsschrift, Rheinische Friedrich-Wilhelms-Universität, Bonn, 1989.
Wilbrink J. Erratic behavior of invariant circles in standard-like mappings. Physica D, 1987, 26(1–3), 358–368.
Yamaguchi Y., Tanikawa K. A remark on the smoothness of critical KAM curves in the standard mapping. Progress Theor. Phys., 1999, 101(1), 1–24.
1963-4
Arnold V. I. Small denominators and problems of stability of motion in classical and celestial mechanics. Uspekhi Mat. Nauk, 1963, 18(6), 91–192 (in Russian). [The English translation: Russian Math. Surveys, 1963, 18(6), 85–191.]
1963-5
Arnold V. I. Small denominators and problems of stability of motion in classical and celestial mechanics. Uspekhi Mat. Nauk, 1963, 18(6), 91–192 (in Russian). [The English translation: Russian Math. Surveys, 1963, 18(6), 85–191.]
1963-6
Arnold V. I., Krylov A. L. Uniform distribution of points on a sphere and some ergodic properties of solutions of linear ordinary differential equations in a complex region. Dokl. Akad. Nauk SSSR, 1963, 148(1), 9–12 (in Russian). [The English translation: Sov. Math. Dokl., 1963, 4(1), 1–5.]
Reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 47–53.
1963-6 — V. I. Arnold
Arnold V. I. Small denominators and problems of stability of motion in classical and celestial mechanics. Russian Math. Surveys, 1963, 18(6), 85–191.
Arnold V. I. Conditions for the applicability and estimate of the error of an averaging method for systems which pass through the states of resonance in the course of their evolution. Sov. Math. Dokl., 1965, 6, 331–334. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 69–74.]
Arnold V. I. The asymptotic Hopf invariant and its applications. In: Proceedings of the All-Union School on Differential Equations with Infinitely Many Independent Variables and on Dynamical Systems with Infinitely Many Degrees of Freedom (Dilizhan, May 21–June 3, 1973). Yerevan: AS of Armenian SSR, 1974, 229–256 (in Russian). [The English translation: Selecta Math. Sov., 1986, 5(4), 327–345.] [The Russian original is reprinted and supplemented in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 215–236.]
Arnold V. I. Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd edition. New York: Springer, 1988. (Grundlehren der Mathematischen Wissenschaften, 250.) [The Russian original 1978.]
Arnold V. I. Remarks on quasicrystallic symmetries. Physica D, 1988, 33(1–3), 21–25.
Arnold V. I. Remarks on quasicrystallic symmetry. Appendix B in: Klein F. Lectures on the Icosahedron and Solution of Equations of Fifth Degree. Moscow: Nauka, 1989, 291–300 (in Russian). [Reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 413–423.]
Arnold V. I. Dynamics of complexity of intersections. Bol. Soc. Brasil. Mat. (N. S.), 1990, 21(1), 1–10. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 489–499.]
Arnold V. I. Bounds for Milnor numbers of intersections in holomorphic dynamical systems. In: Topological Methods in Modern Mathematics. Proceedings of the symposium in honor of John Milnor's sixtieth birthday (Stony Brook, NY, 1991). Editors: L. R. Goldberg and A. V. Phillips. Houston, TX: Publish or Perish, 1993, 379–390.
Arnold V. I. Mathematical methods in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden, and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math., 100.) [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.]
Arnold V. I. Weak asymptotics for the numbers of solutions of Diophantine problems. Funct. Anal. Appl., 1999, 33(4), 292–293.
Arnold V. I. The statistic of the first digits of the deuce powers and repartition of the World. In: Soft and Rigid Mathematical Models. Moscow: Moscow Center for Continuous Mathematical Education Press, 2000, 22–26 (in Russian). [The German translation: Die Mathematik und die Neue Teilung der Welt. Hamburger Mosaik, 2002, No. 5, 65–68.]
Arnold V. I. Continued Fractions. Moscow: Moscow Center for Continuous Mathematical Education Press, 2001 (in Russian). (“Mathematical Education” Library, 14.)
Arnold V. I. Optimization in mean and phase transitions in controlled dynamical systems. Funct. Anal. Appl., 2002, 36(2), 83–92.
Arnold V. I. The longest curves of given degree and the quasicrystallic Harnack theorem in pseudoperiodic topology. Funct. Anal. Appl., 2002, 36(3), 165–171.
Arnold V. I. On a variational problem connected with phase transitions of means in controllable dynamical systems. In: Nonlinear Problems in Mathematical Physics and Related Topics I. In honour of Professor O. A. Ladyzhenskaya. Editors: M. Sh. Birman, S. Hildebrandt, V. A. Solonnikov and N. N. Ural'tseva. Dordrecht: Kluwer Acad. Publ., 2002, 23–34. (Internat. Math. Ser., 1.)
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
Arnold V. I., Kozlov V. V., NeĬshtadt A. I. Mathematical Aspects of Classical and Celestial Mechanics, 2nd edition. Berlin: Springer, 1993. (Encyclopædia Math. Sci., 3; Dynamical Systems, III.) [The Russian original 1985.] [The second, revised and supplemented, Russian edition 2002.]
Gusein-Zade S. M. The number of critical points of a quasiperiodic potential. Funct. Anal. Appl., 1989, 23(2), 129–130.
Gusein-Zade S. M. On the topology of quasiperiodic functions. In: Pseudoperiodic Topology. Editors: V. Arnold, M. Kontsevich and A. Zorich. Providence, RI: Amer. Math. Soc., 1999, 1–7. (AMS Transl., Ser. 2, 197; Adv. Math. Sci., 46.)
Kontsevich M. L., Sukhov Yu. M. Statistics of Klein polyhedra and multidimensional continued fractions. In: Pseudoperiodic Topology. Editors: V. Arnold, M. Kontsevich and A. Zorich. Providence, RI: Amer. Math. Soc., 1999, 9–27. (AMS Transl., Ser. 2, 197; Adv. Math. Sci., 46.)
Novikov S. P. The analytic generalized Hopf invariant. Multivalued functionals. Russian Math. Surveys, 1984, 39(5), 113–124.
1963-6 — R. I. Grigorchuk
Bewley T. Sur l'application des théorèmes ergodiques aux groupes libres de transformations: un contre-exemple. C. R. Acad. Sci. Paris, Sér. A–B, 1970, 270, A1533–A1534.
Bufetov A. I. Operator ergodic theorems for actions of free semigroups and groups. Funct. Anal. Appl., 2000, 34(4), 239–251.
Grigorchuk R. I. An individual ergodic theorem for free group actions. In: XII School on Operator Theory in Function Spaces (Tambov, 1987). Part 1. Tambov: Tambov State Pedagogical Institute, 1987, 57 (in Russian).
Grigorchuk R. I. Ergodic theorems for the actions of a free group and a free semigroup. Math. Notes, 1999, 65(5), 654–657.
Krengel W. Ergodic Theorems. Berlin — New York: Walter de Gruyter, 1986.
Lindenstrauss E. Pointwise theorems for amenable groups. Electron. Res. Announc. Amer. Math. Soc., 1999, 5, 82–90 (electronic); Invent. Math., 2001, 146(2), 259–295.
Nevo A. On discrete groups and pointwise ergodic theory. In: Random Walks and Discrete Potential Theory (Cortona, 1997). Cambridge: Cambridge University Press, 1999, 279–305. (Sympos. Math., 39.)
Nevo A., Stein E. M. A generalization of Birkhoff's pointwise ergodic theorem. Acta Math., 1994, 173, 135–154.
Tempelman A. Ergodic Theorems for Group Actions. Informational and Thermodynamical Aspects. Dordrecht: Kluwer Acad. Publ., 1992. (Math. Appl., 78.) [Revised from the Russian original 1986.]
1963-7
Arnold V. I., Krylov A. L. Uniform distribution of points on a sphere and some ergodic properties of solutions of linear ordinary differential equations in a complex region. Dokl. Akad. Nauk SSSR, 1963, 148(1), 9–12 (in Russian). [The English translation: Sov. Math. Dokl., 1963, 4(1), 1–5.]
Reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 47–53.
1963-7 — R. I. Grigorchuk
Grigorchuk R. I. On the uniform distribution of orbits of actions of hyperbolic groups, in preparation.
1963-8
Arnold V. I., Krylov A. L. Uniform distribution of points on a sphere and some ergodic properties of solutions of linear ordinary differential equations in a complex region. Dokl. Akad. Nauk SSSR, 1963, 148(1), 9–12 (in Russian). [The English translation: Sov. Math. Dokl., 1963, 4(1), 1–5.]
Reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 47–53.
1963-8 — R. I. Grigorchuk
Guivarch Y. Equirepartition dans les espaces homogènes. In: Théorie ergodique (Actes Journées Ergodiques, Rennes, 1973/1974). Editors: J. P. Couze and M. S. Keane. New York: Springer, 1976, 131–142. (Lecture Notes in Math., 532.)
Kazhdan D. A. The uniform distribution on the plane. Trudy Moskov. Mat. Obshch., 1965, 14, 299–305 (in Russian).
Vorobets Ya. B. On the uniform distribution of orbits of free group and semigroup actions on a plane. Proc. Steklov Inst. Math., 2000, 231, 59–89.
1963-9
Arnold V. I., Krylov A. L. Uniform distribution of points on a sphere and some ergodic properties of solutions of linear ordinary differential equations in a complex region. Dokl. Akad. Nauk SSSR, 1963, 148(1), 9–12 (in Russian). [The English translation: Sov. Math. Dokl., 1963, 4(1), 1–5.]
Reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 47–53.
1963-9 — R. I. Grigorchuk
Margulis G. A., Nevo A., Stein E. Analogs of Wiener's ergodic theorems for semisimple Lie groups, II. Duke Math. J., 2000, 103(2), 233–259.
Nevo A. Pointwise ergodic theorems for radial averages on simple Lie groups, I. Duke Math. J., 1994, 76(1), 113–140.
Nevo A. Pointwise ergodic theorems for radial averages on simple Lie groups, II. Duke Math. J., 1997, 86(2), 239–259.
Nevo A., Stein E. Analogs of Wiener's ergodic theorems for semisimple groups, II. Ann. Math., Ser. 2, 1997, 145(3), 565–595.
Nevo A., Thangarelu S. Pointwise ergodic theorems for radial averages on the Heisenberg group. Adv. Math., 1997, 127(2), 307–334.
1963-10
Arnold V. I., Krylov A. L. Uniform distribution of points on a sphere and some ergodic properties of solutions of linear ordinary differential equations in a complex region. Dokl. Akad. Nauk SSSR, 1963, 148(1), 9–12 (in Russian). [The English translation: Sov Math. Dokl., 1963, 4(1), 1–5.]
Reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 47–53.
1963-11
Arnold V. I., Krylov A. L. Uniform distribution of points on a sphere and some ergodic properties of solutions of linear ordinary differential equations in a complex region. Dokl. Akad. Nauk SSSR, 1963, 148(1), 9–12 (in Russian). [The English translation: Sov. Math. Dokl., 1963, 4(1), 1–5.]
Reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 47–53.
1963-12
Arnold V. I., Krylov A. L. Uniform distribution of points on a sphere and some ergodic properties of solutions of linear ordinary differential equations in a complex region. Dokl. Akad. Nauk SSSR, 1963, 148(1), 9–12 (in Russian). [The English translation: Sov. Math. Dokl., 1963, 4(1), 1–5.]
Reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 47–53.
1965-1
Arnold V. I. Sur une propriété topologique des applications globalement canoniques de la mécanique classique. C. R. Acad. Sci. Paris, 1965, 261(19), 3719–3722.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 81–86.
1965-2
Arnold V. I. Sur une propriété topologique des applications globalement canoniques de la mécanique classique. C. R. Acad. Sci. Paris, 1965, 261(19), 3719–3722.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 81–86.
1965-3
Arnold V. I. Sur une propriété topologique des applications globalement canoniques de la mécanique classique. C. R. Acad. Sci. Paris, 1965, 261(19), 3719–3722.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 81–86.
1966-1
Arnold V. I. The stability problem and ergodic properties of classical dynamical systems. In: Proceedings of the International Congress of Mathematicians (Moscow, 1966). Moscow: Mir, 1968, 387–392 (in Russian). [The English translation: AMS Transl., Ser. 2, 1968, 70, 5–11.]
The original is reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 95–101.
1966-2
Arnold V. I. The stability problem and ergodic properties of classical dynamical systems. In: Proceedings of the International Congress of Mathematicians (Moscow, 1966). Moscow: Mir, 1968, 387–392 (in Russian). [The English translation: AMS Transl., Ser. 2, 1968, 70, 5–11.]
The original is reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 95–101.
1966-2 — M. B. Sevryuk
Bambusi D. A Nekhoroshev-type theorem for the Pauli-Fierz model of classical electrodynamics. Ann. Institut Henri Poincaré, Physique théorique, 1994, 60(3), 339–371.
Bambusi D. Exponential stability of breathers in Hamiltonian networks of weakly coupled oscillators. Nonlinearity, 1996, 9(2), 433–457.
Bambusi D. Long time stability of some small amplitude solutions in nonlinear Schrödinger equations. Commun. Math. Phys., 1997, 189(1), 205–226.
Bambusi D. Nekhoroshev theorem for small amplitude solutions in nonlinear Schrödinger equations. Math. Z., 1999, 230(2), 345–387.
Bambusi D. On long time stability in Hamiltonian perturbations of non-resonant linear PDEs. Nonlinearity, 1999, 12(4), 823–850.
Bambusi D., Giorgilli A. Exponential stability of states close to resonance in infinite-dimensional Hamiltonian systems. J. Stat. Phys., 1993, 71(3–4), 569–606.
Bambusi D., Nekhoroshev N. N. A property of exponential stability in nonlinear wave equations near the fundamental linear mode. Physica D, 1998, 122(1–4), 73–104.
Benettin G., Fassò F., Guzzo M. Nekhoroshev-stability of L4 and L5 in the spatial restricted three-body problem. Reg. Chaot. Dynamics, 1998, 3(3), 56–72; erratum: 1998, 3(4), 48.
Benettin G., Fröhlich J., Giorgilli A. A Nekhoroshev-type theorem for Hamiltonian systems with infinitely many degrees of freedom. Commun. Math. Phys., 1988, 119(1), 95–108.
Benettin G., Galgani L., Giorgilli A. A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems. Celest. Mech., 1985, 37(1), 1–25.
Benettin G., Gallavotti G. Stability of motions near resonances in quasi-integrable Hamiltonian systems. J. Stat. Phys., 1986, 44(3–4), 293–338.
Celletti A., Chierchia L. On the stability of realistic three-body problems. Commun. Math. Phys., 1997, 186(2), 413–449.
Celletti A., Ferrara L. An application of the Nekhoroshev theorem to the restricted three-body problem. Celest. Mech. Dynam. Astronom., 1996, 64(3), 261–272.
Chirikov B. V. A universal instability of many-dimensional oscillator systems. Phys. Rep., 1979, 52(5), 263–379.
Delshams A., Gutiérrez P. Effective stability for nearly integrable Hamiltonian systems. In: Proceedings of Intern. Conf. on Differential Equations (\(Equa\tfrac{{\partial i}} {{\partial t}}ff{\text{ 91}}\)) (Barcelona, 1991), Vol. 1. Editors: C. Perelló, C. Simó and J. Solà-Morales. Singapore: World Scientific, 1993, 415–420.
Delshams A., Gutiérrez P. Nekhoroshev and KAM theorems revisited via a unified approach. In: Hamiltonian Mechanics: Integrability and Chaotic Behavior (Toruń, 1993). Editor: J. Seimenis. New York: Plenum Press, 1994, 299–306. (NATO Adv. Sci. Inst. Ser. B Phys., 331.)
Delshams A., Gutiérrez P. Effective stability and KAM theory. J. Differ. Equations, 1996, 128(2), 415–490.
Fassò F., Guzzo M., Benettin G. Nekhoroshev-stability of elliptic equilibria of Hamiltonian systems. Commun. Math. Phys., 1998, 197(2), 347–360.
Gabern F., Jorba À. A restricted four-body model for the dynamics near the Lagrangian points of the Sun-Jupiter system. Discrete Contin. Dynam. Systems, Ser. B, 2001, 1(2), 143–182.
Giorgilli A. Energy equipartition and Nekhoroshev-type estimates for large systems. In: Hamiltonian Dynamical Systems: History, Theory, and Applications (Cincinnati, 1992). Editors: H. S. Dumas, K. R. Meyer and D. S. Schmidt. New York: Springer, 1995, 147–161. (The IMA Volumes in Math. and Appl., 63.)
Giorgilli A. On the problem of stability for near to integrable Hamiltonian systems. In: Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998). Doc. Math., 1998, Extra Vol. III, 143–152 (electronic).
Giorgilli A., Delshams A., Fontich E., Galgani L., Simó C. Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem. J. Differ. Equations, 1989, 77(1), 167–198.
Giorgilli A., Galgani L. Rigorous estimates for the series expansions of Hamiltonian perturbation theory. Celest. Mech., 1985, 37(2), 95–112.
Giorgilli A., Morbidelli A. Invariant KAM tori and global stability for Hamiltonian systems. Z. Angew. Math. Phys., 1997, 48(1), 102–134.
Giorgilli A., Skokos CH. On the stability of the Trojan asteroids. Astron. Astrophys., 1997, 317, 254–261.
Guzzo M. Nekhoroshev stability of quasi-integrable degenerate Hamiltonian systems. Reg. Chaot. Dynamics, 1999, 4(2), 78–102.
Guzzo M., Benettin G. A spectral formulation of the Nekhoroshev theorem and its relevance for numerical and experimental data analysis. Discrete Contin. Dynam. Systems, Ser. B, 2001, 1(1), 1–28.
Guzzo M., Fassò F., Benettin G. On the stability of elliptic equilibria. Math. Phys. Electron. J., 1998, 4, Paper 1, 16 pp. (electronic).
Guzzo M., Lega E., Froeschlé C. On the numerical detection of the effective stability of chaotic motions in quasi-integrable systems. Physica D, 2002, 163(1–2), 1–25.
Guzzo M., Morbidelli A. Construction of a Nekhoroshev like result for the asteroid belt dynamical system. Celest. Mech. Dynam. Astronom., 1996/97, 66(3), 255–292.
Il'yashenko Yu. S. A steepness test for analytic functions. Russian Math. Surveys, 1986, 41(1), 229–230.
Jorba À., Simó C. Effective stability for periodically perturbed Hamiltonian systems. In: Hamiltonian Mechanics: Integrability and Chaotic Behavior (Toruń, 1993). Editor: J. Seimenis. New York: Plenum Press, 1994, 245–252. (NATO Adv. Sci. Inst. Ser. B Phys., 331.)
Jorba À., Villanueva J. On the normal behaviour of partially elliptic lower-dimensional tori of Hamiltonian systems. Nonlinearity, 1997, 10(4), 783–822.
Jorba À., Villanueva J. Numerical computation of normal forms around some periodic orbits of the restricted three-body problem. Physica D, 1998, 114(3–4), 197–229.
Jorba À., Villanueva J. Effective stability around periodic orbits of the spatial RTBP. In: Hamiltonian Systems with Three or More Degrees of Freedom (S'garó, 1995). Editor: C. Simó. Dordrecht: Kluwer Acad. Publ., 1999, 628–632. (NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 533.)
Landis E. E. Uniform steepness indices. Uspekhi Mat. Nauk, 1986, 41(4), 179 (in Russian).
Lochak P. Canonical perturbation theory via simultaneous approximation. Russian Math. Surveys, 1992, 47(6), 57–133.
Lochak P. Hamiltonian perturbation theory: periodic orbits, resonances and intermittency. Nonlinearity, 1993, 6(6), 885–904.
Lochak P. Stability of Hamiltonian systems over exponentially long times: the near-linear case. In: Hamiltonian Dynamical Systems: History, Theory, and Applications (Cincinnati, 1992). Editors: H. S. Dumas, K. R. Meyer and D. S. Schmidt. New York: Springer, 1995, 221–229. (The IMA Volumes in Math. and Appl., 63.)
Lochak P., NeĬshtadt A. I., Estimates of stability time for nearly integrable systems with a quasiconvex Hamiltonian. Chaos, 1992, 2(4), 495–499.
Lochak P., NeĬshtadt A. I., Niederman L. Stability of nearly integrable convex Hamiltonian systems over exponentially long times. In: Seminar on Dynamical Systems (St. Petersburg, 1991). Editors: S. B. Kuksin, V. F. Lazutkin and J. Pöschel. Basel: Birkhäuser, 1994, 15–34.
Morbidelli A. Bounds on diffusion in phase space: connection between Nekhoroshev and KAM theorems and superexponential stability of invariant tori. In: Hamiltonian Systems with Three or More Degrees of Freedom (S'Agaró, 1995). Editor: C. Simó. Dordrecht: Kluwer Acad. Publ., 1999, 514–517. (NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 533.)
Morbidelli A., Giorgilli A. Quantitative perturbation theory by successive elimination of harmonics. Celest. Mech. Dynam. Astronom. 1993, 55(2), 131–159.
Morbidelli A., Giorgilli A. On a connection between KAM and Nekhoroshev’ theorems. Physica D, 1995, 86(3), 514–516.
Morbidelli A., Giorgilli A. Superexponential stability of KAM tori. J. Stat. Phys., 1995, 78(5–6), 1607–1617.
Morbidelli A., Guzzo M. The Nekhoroshev theorem and the asteroid belt dynamical system. Celest. Mech. Dynam. Astronom., 1996/97, 65(1–2), 107–136.
Nekhoroshev N. N. On the behavior of Hamiltonian systems close to integrable ones. Funct. Anal. Appl., 1971, 5(4), 338–339.
Nekhoroshev N. N. Stable lower estimates for smooth mappings and the gradients of smooth functions. Math. USSR, Sb., 1973, 19(3), 425–467.
Nekhoroshev N. N. The method of successive canonical changes of variables. An addendum to: Moser J. Lectures on Hamiltonian Systems. Moscow: Mir, 1973, 150–164 (in Russian).
Nekhoroshev N. N. An exponential estimate of the stability time for Hamiltonian systems close to integrable ones, I. Russian Math. Surveys, 1977, 32(6), 1–65.
Nekhoroshev N. N. An exponential estimate of the stability time for Hamiltonian systems close to integrable ones, II. Trudy Semin. Petrovskogo, 1979, 5, 5–50 (in Russian). [The English translation in: Topics in Modern Mathematics. Editor: O. A. Oleĭnik. New York: Consultant Bureau, 1985, 1–58. (Petrovskiĭ Semin., 5.)]
Nekhoroshev N. N. Exponential stability of the approximate fundamental mode of a nonlinear wave equation. Funct. Anal. Appl., 1999, 33(1), 69–71.
Nekhoroshev N. N. Strong stability of the approximate fundamental mode of a nonlinear string equation. Trudy Moskov. Mat. Obshch., 2002, 63, 166–236 (in Russian, for the English translation see Trans. Moscow Math. Soc.).
Niederman L. Stability over exponentially long times in the planetary problem. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-body Dynamical Systems (Cortina d'Ampezzo, 1993). Editors: A. E. Roy and B. A. Steves. New York: Plenum Press, 1995, 109–118. (NATO Adv. Sci. Inst. Ser. B Phys., 336.)
Niederman L. Stability over exponentially long times in the planetary problem. Nonlinearity, 1996, 9(6), 1703–1751.
Niederman L. Nonlinear stability around an elliptic equilibrium point in a Hamiltonian system. Nonlinearity, 1998, 11(6), 1465–1479.
Perry A. D., Wiggins S. KAM tori are very sticky: rigorous lower bounds on the time to move away from an invariant Lagrangian torus with linear flow. Physica D, 1994, 71(1–2), 102–121.
Pöschel J. Nekhoroshev estimates for quasi-convex Hamiltonian systems. Math. Z., 1993, 213(2), 187–216.
Pöschel J. On Nekhoroshev estimates for a nonlinear Schrödinger equation and a theorem by Bambusi. Nonlinearity, 1999, 12(6), 1587–1600.
Pöschel J. On Nekhoroshev's estimate at an elliptic equilibrium. Internal. Math. Res. Notices, 1999, 4, 203–215.
Rosikov Yu. V. The normalization of a perturbed system of Hamiltonian equations in the resonant case. Preprint of the Moscow Space Research Institute, Russia Academy of Sciences, 1994, № 1892, 37 pp. (in Russian).
Rosikov Yu. V. A refinement of the exponential estimate on the stability time in nearly integrable Hamiltonian systems. Preprint of the Moscow Space Research Institute, Russia Academy of Sciences, 1994, № 1893, 34 pp. (in Russian).
Steichen D., Giorgilli A. Long time stability for the main problem of artificial satellites. Celest. Mech. Dynam. Astronom. 1997/98, 69(3), 317–330.
Vecheslavov V. V., Chirikov B. V. What is the rate of the Arnold diffusion equal to? Preprint of the Novosibirsk Institute for Nuclear Physics, the USSR Academy of Sciences, 1989, № 72 (in Russian).
1966-3
Arnold V. I. The stability problem and ergodic properties of classical dynamical systems. In: Proceedings of the International Congress of Mathematicians (Moscow, 1966). Moscow: Mir, 1968, 387–392 (in Russian). [The English translation: AMS Transl., Ser. 2, 1968, 70, 5–11.]
The original is reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 95–101.
1966-4
Arnold V. I. The stability problem and ergodic properties of classical dynamical systems. In: Proceedings of the International Congress of Mathematicians (Moscow, 1966). Moscow: Mir, 1968, 387–392 (in Russian). [The English translation: AMS Transl., Ser. 2, 1968, 70, 5–11.]
The original is reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 95–101.
Arnold V. I. Sur une propriété topologique des applications globalement canoniques de la mécanique classique. C. R. Acad. Sci. Paris, 1965, 261(19), 3719–3722.
The Russian translation in: [2b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 81–86.
1966-5
Arnold V. I. The stability problem and ergodic properties of classical dynamical systems. In: Proceedings of the International Congress of Mathematicians (Moscow, 1966). Moscow: Mir, 1968, 387–392 (in Russian). [The English translation: AMS Transl., Ser. 2, 1968, 70, 5–11.]
The original is reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 95–101.
Arnold V. I. Sur une propriété topologique des applications globalement canoniques de la mécanique classique. C. R. Acad. Sci. Paris, 1965, 261(19), 3719–3722.
The Russian translation in: [2b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 81–86.
1966-6
Arnold V. I. The stability problem and ergodic properties of classical dynamical systems. In: Proceedings of the International Congress of Mathematicians (Moscow, 1966). Moscow: Mir, 1968, 387–392 (in Russian). [The English translation: AMS Transl., Ser. 2, 1968, 70, 5–11.]
The original is reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 95–101.
1969-1 — V. D. Sedykh
Aleksandrov V. A. An example of a flexible polyhedron with nonconstant volume in the spherical space. Beiträge zur Algebra und Geometrie, 1997, 38(1), 11–18.
Connelly R., Sabitov I., Walz A. The bellows conjecture. Beiträge zur Algebra und Geometrie, 1997, 38(1), 1–10.
Sabitov I. Kh. On the problem of the invariance of the volume of a deformable polyhedron. Russian Math. Surveys, 1995, 50(2), 451–452.
1970-1 — M. B. Sevryuk
Arnold V. I. On matrices depending on parameters. Russian Math. Surveys, 1971, 26(2), 29–43. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 155–173.]
Arnold V. I. Lectures on bifurcations and versal families. Russian Math. Surveys, 1972, 27(5), 54–123.
Arnold V. I. Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd edition. New York: Springer, 1988, § 30. (Grundlehren der Mathematischen Wissenschaften, 250.) [The Russian original 1978.]
Braun H., Koecher M. Jordan-Algebren. Berlin: Springer, 1966.
Burgoyne N., Cushman R. Conjugacy classes in linear groups. J. Algebra, 1977, 44(2), 339–362.
Djoković D.Ž., Patera J., Winternitz P., Zassenhaus H. Normal forms of elements of classical real and complex Lie and Jordan algebras. J. Math. Phys., 1983, 24(6), 1363–1374.
Edelman A., Elmroth E., Kågström B. A geometric approach to perturbation theory of matrices and matrix pencils. Part I: versal deformations. SIAM J. Matrix Anal. Appl., 1997, 18(3), 653–692.
Edelman A., Elmroth E., Kågström B. A geometric approach to perturbation theory of matrices and matrix pencils. Part II: a stratification-enhanced staircase algorithm. SIAM J. Matrix Anal. Appl., 1999, 20(3), 667–699.
Ferrer J., García M. I., Puerta F. Brunowsky local form of a holomorphic family of pairs of matrices. Linear Algebra Appl., 1997, 253, 175–198.
Galin D. M. On real matrices depending on parameters. Uspekhi Mat. Nauk, 1972, 27(1), 241–242 (in Russian).
Galin D. M. Versal deformations of linear Hamiltonian systems. Trudy Semin. Petrovskogo, 1975, 1, 63–74 (in Russian). [The English translation: AMS Transl., Ser. 2, 1982, 118, 1–12.]
García-Planas M. I. Versal deformations of pairs of matrices. Linear Algebra Appl., 1992, 170, 194–200.
Hoveijn I. Versal deformations and normal forms for reversible and Hamiltonian linear systems. J. Differ. Equations, 1996, 126(2), 408–442.
Jacobson N. Structure and representations of Jordan algebras. Providence, RI: Amer. Math. Soc., 1968. (Amer. Math. Soc. Colloquium Publ., 39.)
Koçak H. Normal forms and versal deformations of linear Hamiltonian systems. J. Differ. Equations, 1984, 51(3), 359–407.
Melbourne I. Versal unfoldings of equivariant linear Hamiltonian vector fields. Math. Proc. Cambridge Phil. Soc., 1993, 114(3), 559–573.
Patera J., Rousseau C. Complex orthogonal and symplectic matrices depending on parameters. J. Math. Phys., 1982, 23(5), 705–714.
Patera J., Rousseau C. Versal deformations of elements of classical Jordan algebras. J. Math. Phys., 1983, 24(6), 1375–1380.
Patera J., Rousseau C., Schlomiuk D. Dimensions of orbits and strata in complex and real classical Lie algebras. J. Math. Phys., 1982, 23(4), 490–494.
Patera J., Rousseau C., Schlomiuk D. Versal deformations of elements of real classical Lie algebras. J. Phys. A: Math. Gen., 1982, 15(4), 1063–1086.
Sevryuk M. B. Linear reversible systems and their versal deformations. J. Sov. Math., 1992, 60(5), 1663–1680. [The Russian original: Trudy Seminara im. I. G. Petrovskogo, 1991, 15, 33–54.]
Shih C.-W. Normal forms and versal deformations of linear involutive dynamical systems. Chinese J. Math., 1993, 21(4), 333–347.
Wall G. E. On the conjugacy classes in the unitary, symplectic and orthogonal groups. J. Austral. Math. Soc., 1963, 3(1), 1–62.
Wan Y.-H. Versal deformations of infinitesimally symplectic transformations with antisymplectic involutions. In: Singularity Theory and its Applications, Part II. Editors: M. Roberts and I. Stewart. Berlin: Springer, 1991, 301–320. (Lecture Notes in Math., 1463.)
1970-2
Arnold V. I. Algebraic unsolvability of the problem of Lyapunov stability and the problem of topological classification of singular points of an analytic system of differential equations. Funct. Anal. Appl., 1970, 4(3), 173–180.
Arnold V. I. Algebraic unsolvability of the problem of stability and the problem of topological classification of singular points of analytic systems of differential equations. Uspekhi Mat. Nauk, 1970, 25(2), 265–266 (in Russian).
Arnold V. I. Local problems of analysis. Moscow Univ. Math. Bull., 1970, 25(2), 77–80.
1970-3 — V. I. Arnold
Arnold V. I. One-dimensional cohomologies of Lie algebras of nondivergent vector fields and rotation numbers of dynamic systems. Funct. Anal. Appl., 1969, 3(4), 319–321. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 147–150.]
1970-5 — M. B. Sevryuk
arnold V. I. Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd edition. New York: Springer, 1988, § 18. (Grundlehren der Mathematischen Wissenschaften, 250.) [The Russian original 1978.]
Bakhtin V. I. Averaging in multifrequency systems. Funct. Anal. Appl., 1986, 20(2), 83–88.
Bakhtin V. I. Diophantine approximations on images of mappings. Dokl. Akad. Nauk Beloruss. SSR, 1991, 35(5), 398–400 (in Russian).
Bernik V. I. Diophantine approximations on differentiable manifolds. Dokl. Akad. Nauk Beloruss. SSR, 1989, 33(8), 681–683 (in Russian).
Bernik V. I., Mel'nichuk Yu. V. Diophantine Approximations and Hausdorff Dimension. Minsk: Nauka i Tekhnika, 1988 (in Russian).
Broer H. W., Huitema G. B., Sevryuk M. B. Quasi-Periodic Motions in Families of Dynamical Systems: Order amidst Chaos. Berlin: Springer, 1996. (Lecture Notes in Math., 1645.)
Dodson M. M., Pöschel J., Rynne B. P., Vickers J. A. G. The Hausdorff dimension of small divisors for lower-dimensional KAM-tori. Proc. Roy. Soc. London, Ser. A, 1992, 439(1906), 359–371.
Dodson M. M., Vickers J. A. G. Exceptional sets in Kolmogorov-Arnold-Moser theory. J. Phys. A: Math. Gen., 1986, 19(3), 349–374.
Parasyuk Ī. O. Persistence of quasi-periodic motions in reversible multifrequency systems. Dokl. Akad. Nauk Ukrain. SSR, Ser. A, 1982, 9, 19–22 (in Russian).
Postnikov A. G., FreĬman G. A. Inter-college symposium on the number theory (Vladimir, June of 1968). Uspekhi Mat. Nauk, 1969, 24(1), 235–237 (in Russian).
Pyartli A. S. Diophantine approximations on submanifolds of the Euclidean space. Funct. Anal. Appl., 1969, 3(4), 303–306.
Schmidt W. M. Diophantine Approximation. Berlin: Springer, 1980. (Lecture Notes in Math., 785.)
Sevryuk M. B. The iteration-approximation decoupling in the reversible KAM theory. Chaos, 1995, 5(3), 552–565.
Sprindžuk V. G. Metric Theory of Diophantine Approximations. New York: John Wiley, 1979. [The Russian original 1977.]
Sprindžuk V. G. Achievements and problems in the theory of Diophantine approximations. Russian Math. Surveys, 1980, 35(4), 1–80.
Xia Zh. Existence of invariant tori in volume-preserving diffeomorphisms. Ergod. Theory Dynam. Systems, 1992, 12(3), 621–631.
1970-6 — A. M. Lukatskiĭ
Arnold V. I. Sur la géométrie différentielle de groupes de Lie de dimension infinie and ses applications à l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier (Grenoble), 1966, 16(1), 319–361.
LukatskiĬ A. M. Curvature of groups of diffeomorphisms preserving the measure of the 2-sphere. Funct. Anal. Appl., 1979, 13(3), 174–177.
Misiołek G. Stability of flows of ideal fluids and the geometry of the group of diffeomorphisms. Indiana Univ. Math. J., 1993, 42(1), 215–235.
Misiołek G. Conjugate points in Dμ(\(\mathbb{T}^2 \)). Proc. Amer. Math. Soc., 1996, 124(3), 977–982.
1970-7 — A. M. Lukatskiĭ
Arakelyan T. A., Savvidy G. K. Geometry of a group of area-preserving diffeomorphisms. Phys. Lett. B, 1989, 223(1), 41–46.
Kambe T., Nakamura F., Hattori Y. Kinematical instability and line-stretching in relation to the geodesics of fluid motion. In: Topological Aspects of the Dynamics of Fluids and Plasmas. Editors: H. K. Moffatt, G. M. Zaslavsky, P. Comte and M. Tabor. Dordrecht: Kluwer Acad. Publ., 1992, 493–504. (NATO Adv. Sci. Inst. Ser. E Appl. Sci., 218.)
LukatskiĬ A. M. Curvature of groups of diffeomorphisms preserving the measure of the 2-sphere. Funct. Anal. Appl., 1979, 13(3), 174–177.
LukatskiĬ A. M. Curvature of the group of measure-preserving diffeomorphisms of the n-dimensional torus. Sib. Math. J., 1984, 25(6), 893–903.
LukatskiĬ A. M. Structure of the curvature tensor of the group of measure-preserving diffeomorphisms of a compact two-dimensional manifold. Sib. Math. J., 1988, 29(6), 947–951.
Yoshida K. Riemannian curvature on the group of area-preserving diffeomorphisms (motions of fluid) of 2-sphere. Physica D, 1997, 100(3–4), 377–389.
1970-8
Faddeev L. D. On the theory of stability for stationary plane-parallel currents of an ideal fluid. Zap. Nauch. Semin. Leningrad. Otd. Mat. Inst. Steklova, 1971, 21, 164–172 (in Russian). (Boundary Problems of Mathematical Physics and Related Questions of the Function Theory, 5.)
1970-9 — A. M. Lukatskiĭ
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
1970-10 — V. I. Arnold, B. A. Khesin
Nikishin N. A. Fixed points of diffeomorphisms of two-dimensional spheres preserving oriented area. Funct. Anal. Appl., 1974, 8(1), 77–79.
Simon C. P. A bound for the fixed-point index of an area-preserving map with applications to mechanics. Invent. Math., 1974, 26(3), 187–200.
1970-13 — V. A. Vassiliev
Arnold V. I. On some topological invariants of algebraic functions. Trans. Moscow Math. Soc., 1970, 21, 30–52.
Kharlamov V. M. Rigid isotopy classification of real plane curves of degree 5. Funct. Anal. Appl., 1981, 15(1), 73–74.
Looijenga E. J. N. Cohomology of M3 and M 31 . In: Mapping Class Groups and Moduli Spaces of Riemann Surfaces (Göttingen/Seattle, WA, 1991). Editors: C.-F. Bödigheimer and R. M. Hain. Providence, RI: Amer. Math. Soc., 1993, 205–228. (Contemp. Math., 150.)
Vassiliev V. A. How to calculate homology groups of spaces of nonsingular algebraic projective hypersurfaces. Proc. Steklov Inst. Math., 1999, 225, 121–140.
1970-14 — M. L. Kontsevich
Hatcher A., McCullough D. Finiteness of classifying spaces of relative diffeomorphism groups of 3-manifolds. Geometry & Topology, 1997, 1, 91–109 (electronic). [Internet: http:/www.arXiv.org/abs/math.GT/9712260]
Hatcher A. Spaces of knots. [Internet: http:/www.arXiv.org/abs/math.GT/9909095]
1970-14 — V. A. Vassiliev
Goldsmith D. Motions of links in the 3-sphere. Bull. Amer. Math. Soc., 1974, 80, 62–66; Math. Scand., 1982, 50, 167–205.
Hatcher A. Topological moduli spaces of knots. [Internet: http://www.math.cornell.edu/~hatcher/Papers/]
Tourtchine V. Sur l'homologie des espaces des nœuds non-compacts. [Internet: http:/www.arXiv.org/abs/math.QA/0010017]
Vassiliev V. A. Cohomology of knot spaces. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 23–69. (Adv. Sov. Math., 1.)
Vassiliev V. A. Topology of two-connected graphs and homology of spaces of knots. In: Differential and Symplectic Topology of Knots and Curves. Editor: S. Tabachnikov. Providence, RI: Amer. Math. Soc., 1999, 253–286. (AMS Transl., Ser. 2, 190; Adv. Math. Sci., 42.)
Vassiliev V. A. Combinartorial formulae for cohomology of knot spaces. Moscow Math. J., 2001, 1(1), 91–123.
1970-15 — V. V. Goryunov
Goryunov V. V. Functions on space curves. J. London Math. Soc., Ser. 2, 2000, 61(3), 807–822.
Goryunov V. V. Simple functions on space curves. Funct. Anal. Appl., 2000, 34(2), 129–132.
Goryunov V. V., Lando S. K. On enumeration of meromorphic functions on the line. In: The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (Toronto, 1997). Editors: E. Bierstone, B. A. Khesin, A. G. Khovanskiĭ and J. E. Marsden. Providence, RI: Amer. Math. Soc., 1999, 209–223. (Fields Inst. Commun., 24.)
Mond D., van Straten D. Milnor number equals Tjurina number for functions on space curves. J. London Math. Soc., Ser. 2, 2001, 63(1), 177–187.
van Straten D. Private communication.
1970-15 — S. K. Lando
Arnold V. I. Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges. Funct. Anal. Appl., 1996, 30(1), 1–14.
Arnold V. I. Critical points of functions and the classification of caustics. Uspekhi Mat. Nauk, 1974, 29(3), 243–244 (in Russian). [Reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 213–214.]
Crescimanno M., Taylor W. Large N phases of chiral QCD2. Nuclear Phys. B, 1995, 437(1), 3–24.
Dubrovin B. A. Geometry of 2D topological field theories. In: Integrable Systems and Quantum Groups (Montecatini Terme, 1993). Editors: M. Francaviglia and S. Greco. Berlin: Springer and Florence: Centro Internazionale Matematico Estivo, 1996, 120–348. (Lecture Notes in Math., 1620; Fondazione C. I. M. E.)
Ekedahl T., Lando S. K., Shapiro M. Z., Vainshtein A. D. On Hurwitz numbers and Hodge integrals. C. R. Acad. Sci. Paris, Sér. I Math., 1999, 328(12), 1175–1180.
Ekedahl T., Lando S. K., Shapiro M. Z., Vainshtein A. D. Hurwitz numbers and intersections on moduli spaces of curves. Invent. Math., 2001, 146(2), 297–327.
El Marraki M., Hanusse N., Zipperer J., Zvonkine A. D. Cacti, braids and complex polynomials. Sémin. Lotharing. de Combinatoire, 1997, 37, Art. B37b, 36 pp. (electronic). [Internet: http://www-irma.u-strasbg.fr/EMIS/journals/SLC]
Goryunov V. V., Lando S. K. On enumeration of meromorphic functions on the line. In: The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (Toronto, 1997). Editors: E. Bierstone, B. A. Khesin, A. G. Khovanskiĭ and J. E. Marsden. Providence, RI: Amer. Math. Soc., 1999, 209–223. (Fields Inst. Commun., 24.)
Goulden I. P., Jackson D. M. The combinatorial relationship between trees, cacti and certain connection coefficients for the symmetric group. European J. Combinatorics, 1992, 13(5), 357–365.
Goulden I. P., Jackson D. M. Transitive factorization into transpositions, and holomorphic mappings on the sphere. Proc. Amer. Math. Soc., 1997, 125(1), 51–60.
Goulden I. P., Jackson D. M., Vainshtein A. D. The number of ramified coverings of the sphere by the torus and surfaces of higher genera. [Internet: http://www.arXiv.org/abs/math.AG/9902125]
Graber T., Pandharipande R. Localization of virtual classes. [Internet: http://www.arXiv.org/abs/math.AG/9708001]
Hurwitz A. Über Riemann'sche Flächen mit gegebenen Verzweigungspunkten. Math. Ann., 1891, 39(1), 1–61.
Lando S. K., Zvonkine D. A. On multiplicities of the Lyashko-Looijenga mapping on the discriminant strata. Funct. Anal. Appl., 1999, 33(3), 178–188.
Looijenga E. J. N. The complement of the bifurcation variety of a simple singularity. Invent. Math., 1974, 23(2), 105–116.
Lyashko O. V. Geometry of bifurcation diagrams. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics, Vol. 22. Moscow: VINITI, 1983, 99–129 (in Russian). [The English translation: J. Sov. Math., 1984, 27, 2736–2759.]
Mednykh A. D. Determination of the number of nonsingular coverings of a compact Riemann surface. Sov. Math. Dokl., 1978, 239(2), 269–271.
Mednykh A. D. Branched coverings of Riemann surfaces whose branch orders coincide with the multiplicity. Commun. Algebra, 1990, 18(5), 1517–1533.
Natanzon S. M. Topology of 2-dimensional coverings and meromorphic functions on real and complex algebraic curves. Trudy Semin. Vekt. Tenz. Anal., 1988, 23, 79–103 (in Russian) [The English translation: Selecta Math. Sov., 1993, 12(3), 251–291.]
Strehl V. Minimal transitive products of transpositions: the reconstruction of a proof by A. Hurwitz. Sémin. Lotharing. de Combinatorie, 1996, 37, Art. B37c, 12 pp. (electronic). [Internet: http://www-irma.u-strasbg.fr/EMIS/journals/SLC]
Shapiro B. Z., Shapiro M. Z., Vainshtein A. D. Ramified coverings of S2 with one degenerate branching point and enumeration of edge-oriented graphs. In: Topics in Singularity Theory. V. I. Arnold's 60th Anniversary Collection. Editors: A. Khovanskiĭ, A. Varchenko and V. Vassiliev. Providence, RI: Amer. Math. Soc., 1997, 219–227. (AMS Transl., Ser. 2, 180; Adv. Math. Sci., 34.)
Zdravkovska S. The topological classification of polynomial mappings. Uspekhi Mat. Nauk, 1970, 25(4), 179–180 (in Russian).
Zvonkine D. A. Multiplicities of the Lyashko-Looijenga map on its strata. C. R. Acad. Sci. Paris, Sér. I Math., 1997, 324(12), 1349–1353.
1970-15 — S. M. Natanzon
Arnold V. I. Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges. Funct. Anal. Appl., 1996, 30(1), 1–14.
Diaz S., Edidin D. Towards the homology of Hurwitz spaces. J. Differ. Geom., 1996, 43(1), 66–98.
Dubrovin B. A. Geometry of 2D topological field theories. In: Integrable Systems and Quantum Groups (Montecatini Terme, 1993). Editors: M. Francaviglia and S. Greco. Berlin: Springer, 1996, 120–348. (Lecture Notes in Math., 1620.)
Guest M. A., Kozlowski A., Murayama M., Yamaguchi K. The homotory type of the space of rational functions. J. Math. Kyoto Univ., 1995, 35(4), 631–638.
Harris J., Mumford D. On the Kodaira dimension of the moduli space of curves. Invent. Math., 1982, 67(1), 23–86.
Hurwitz A. Über Riemann'sche Flächen mit gegebenen Verzweigungspunkten. Math. Ann., 1891, 39(1), 1–61.
KhovanskiĬ A. G., Zdravkovska S. Branched covers of S2 and braid groups. J. Knot Theory Ramifications, 1996, 5(1), 55–75.
Kontsevich M., Manin Yu. Gromov-Witten classes, quantum cohomology and enumerative geometry. Commun. Math. Phys., 1994, 164(3), 525–562.
Natanzon S. M. Spaces of real meromorphic functions on real algebraic curves. Sov. Math. Dokl., 1984, 30(3), 724–726.
Natanzon S. M. Uniformization of spaces of meromorphic functions. Sov. Math. Dokl., 1986, 33(2), 487–490.
Natanzon S. M. Topology of 2-dimensional coverings and meromorphic functions on real and complex algebraic curves. Trudy Semin. Vekt. Tenz. Anal., 1988, 23, 79–103 (in Russian) [The English translation: Selecta Math. Sov., 1993, 12(3), 251–291.]
Natanzon S. M. Spaces of meromorphic functions on Riemann surfaces. In: Topics in Singularity Theory. V. I. Arnold's 60th Anniversary Collection. Editors: A. Khovanskiĭ, A. Varchenko and V. Vassiliev. Providence, RI: Amer. Math. Soc., 1997, 175–180. (AMS Transl., Ser. 2, 180; Adv. Math. Sci., 34.)
Natanzon S. M. Moduli of real algebraic surfaces and their superanalogues. Differentials, spinors and Jacobians of real curves. Russian Math. Surveys, 1999, 54(6), 1091–1147.
Natanzon S. M. Moduli of Riemann surfaces, Hurwitz-type spaces, and their superanalogues. Russian Math. Surveys, 1999, 54(1), 61–117.
Natanzon S. M., Shadrin S. V. Topological classification of unitary functions of arbitrary genus. Russian Math. Surveys, 2000, 55(6), 1163–1164.
Natanzon S. M., Turaev V. G. A compactification of the Hurwitz space. Topology, 1999, 38(4), 889–914.
Wajnryb B. Orbits of Hurwitz action for coverings of a sphere with two special fibers. Indag. Math. (N. S.), 1996, 7(4), 549–558.
1970-15 — D. A. Zvonkine
Ekedahl T., Lando S., Shapiro M., Vainshtein A. Hurwitz numbers and intersections on moduli spaces of curves. Invent. Math., 2001, 146(2), 297–327.
Goulden I. P., Jackson D. M The combinatorial relationship between trees, cacti and certain connection coefficients for the symmetric group. European J. Combinatorics, 1992, 13(5), 357–365.
Goulden I. P., Jackson D. M. Transitive factorization into transpositions, and holomorphic mappings on the sphere. Proc. Amer. Math. Soc., 1997, 125(1), 51–60.
Goupil A., Schaeffer G. Factoring n-cycles and counting maps of given genus. European J. Combinatorics, 1998, 19(7), 819–834.
Lando S. K., Zvonkine D. A. On multiplicities of the Lyashko-Looijenga mapping on the discriminant strata. Funct. Anal. Appl., 1999, 33(3), 178–188.
Mednykh A. D. Nonequivalent coverings of Riemann surfaces with a prescribed ramification type. Sib. Math. J., 1984, 25(4), 606–625.
Okounkov A., Pandharipande R. Gromov-Witten theory, Hurwitz numbers, and matrix models, I. [Internet: http://www.arXiv.org/abs/math.AG/0101147]
Zvonkine D. A. Transversal multiplicities of the Lyashko-Looijenga map. C. R. Acad. Sci. Paris, Sér. I Math., 1997, 325(6), 589–594.
1970-16
Arnold V. I. Algebraic unsolvability of the problem of Lyapunov stability and the problem of topological classification of singular points of an analytic system of differential equations. Funct. Anal. Appl., 1970, 4(3), 173–180.
Arnold V. I. Algebraic unsolvability of the problem of stability and the problem of topological classification of singular points of analytic systems of differential equations. Uspekhi Mat. Nauk, 1970, 25(2), 265–266 (in Russian).
Arnold V. I. Local problems of analysis. Moscow Univ. Math. Bull., 1970, 25(2), 77–80.
1971-1 — R. I. Bogdanov
Bogdanov R. I. Factorization of diffeomorphisms over phase portraits of vector fields on the plane. Funct. Anal. Appl., 1997, 31(2), 126–128.
1971-2 — M. B. Mishustin
Arnold V. I. Remarks on singularities of finite codimension in complex dynamical systems. Funct. Anal. Appl., 1969, 3(1), 1–5. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 129–137.]
Arnold V. I. Bifurcations of invariant manifolds of differential equations and normal forms in neighborhoods of elliptic curves. Funct. Anal. Appl., 1976, 10(4), 249–259.
Arnold V. I. Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd edition. New York: Springer, 1988. (Grundlehren der Mathematischen Wissenschaften, 250.) [The Russian original 1978.]
Bruno A. D. Normal form of differential equations with a small parameter. Math. Notes, 1974, 16, 832–836.
Burlakova L. A., Irtegov V. D., Novikov M. A. Stability and bifurcations of invariant manifolds of systems of bodies in Newton force field. In: International Aerospace Congress (Moscow, 1994). Moscow: Petrovka, 1994, 232–236.
Il'yashenko Yu. S., Pyartli A. S. Materialization of Poincaré resonances and divergence of normalizing series. Trudy Semin. Petrovskogo, 1981, 7, 3–49 (in Russian). [The English translation: J. Sov. Math., 1985, 31, 3053–3092.]
Johnson M. E., Jolly M. S., Kevrekidis I. G. Two-dimensional invariant manifolds and global bifurcations: some approximation and visualization studies. Numerical Algorithms, 1997, 14(1–3), 125–140.
Llibre J., Nuñes A. Separatrix surfaces and invariant manifolds of a class of integrable Hamiltonian systems and their perturbations. Mem. Amer. Math. Soc., 1994, 107, viii+191 pp.
Pyartli A. S. Birth of complex invariant manifolds close to a singular point of a parametrically dependent vector field. Funct. Anal. Appl., 1972, 6(4), 339–340.
Siberian Branch of Russian Academy of Sciences. Physical and Mathematical Sciences. Scientific report, 2000 (in Russian). [Internet: http://www.sbras.ru/win/sbras/rep/2000/fiz-mat/fmn1.html]
1971-3
Arnold V. I. Problèmes résolubles et problèmes irrésolubles analytiques et géométriques. In: Passion des Formes. Dynamique Qualitative Sémiophysique et Intelligibilité. Dédié à R. Thorn. Fontenay-St Cloud: ENS Éditions, 1994, 411–417; In: Formes et Dynamique, Renaissance d'un Paradigme. Hommage à René Thom. Paris: Eshel, 1995. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 577–582.]
1971-4 — M. B. Sevryuk
Arnold V. I., Kozlov V. V., NeĬshtadt A. I. Mathematical Aspects of Classical and Celestial Mechanics, 2nd edition. Berlin: Springer, 1993, Ch. 7, §5. (Encyclopædia Math. Sci., 3; Dynamical systems, III.) [The Russian original 1985.] [The second, revised and supplemented, Russian edition 2002.]
Karapetyan A. V., Rumyantsev V. V. Stability of Conservative and Dissipative Systems. Itogi Nauki i Tekhniki VINITI. General Mechanics, Vol. 6. Moscow: VINITI, 1983 (in Russian).
Kozlov V. V. Instability of an equilibrium in a potential field. Russian Math. Surveys, 1981, 36(1), 238–239.
Kozlov V. V. On the instability of an equilibrium in a potential field. Russian Math. Surveys, 1981, 36(3), 256–257.
Kozlov V. V. A conjecture on the existence of asymptotic motions in classical mechanics. Funct. Anal. Appl., 1982, 16(4), 303–304.
Kozlov V. V. Asymptotic solutions of the equations of classical mechanics. J. Appl. Math. Mech., 1982, 46(4), 454–457.
Kozlov V. V. Asymptotic motions and the problem on the converse of the Lagrange-Dirichlet theorem. J. Appl. Math. Mech., 1986, 50(6), 719–725.
Kozlov V. V. On a problem by Kelvin. J. Appl. Math. Mech., 1989, 53(1), 133–135.
Kozlov V. V., Furta S. D. Asymptotics of the Solutions of Strongly Nonlinear Systems of Differential Equations. Moscow: Moscow University Press, 1996 (in Russian).
Kozlov V. V., Palamodov V. P. On the asymptotic solutions of the equations of classical mechanics. Sov. Math. Dokl., 1982, 25(2), 335–339.
Lyapunov A. M. The General Problem of the Stability of Motion. London: Taylor & Francis, 1992. [The Russian original 1892.] [The first French translation 1907.]
Lyapunov A. M. On the instability of an equilibrium in some cases where the force function is not a maximum. In: Collected Papers, Vol. II. Moscow-Leningrad: the USSR Academy of Sciences Press, 1956, 391–400 (in Russian). [The original publication 1897.]
Palamodov V. P. On the stability of an equilibrium in a potential field. Funct. Anal. Appl., 1977, 11(4), 277–289.
Palamodov V. P. Stability of motion and algebraic geometry. In: Dynamical Systems in Classical Mechanics. Editor: V. V. Kozlov. Providence, RI: Amer. Math. Soc., 1995, 5–20. (AMS Transl., Ser. 2, 168; Adv. Math. Sci., 25.)
Rouche N., Habets P., Laloy M. Stability Theory by Liapunov's Direct Method. New York: Springer, 1977. (Appl. Math. Sci., 100.)
Rumyantsev V. V., SosnitskiĬ S. P. On the instability of an equilibrium of holonomic conservative systems. J. Appl. Math. Mech., 1993, 57(6), 1101–1122.
Tamm I. E. Basic Electricity Theory, 10th edition. Moscow: Nauka, 1989, Ch. I, § 19 (in Russian).
1971-9 — S. Yu. Yakovenko
Arnold V. I. Dynamics of complexity of intersections. Bol. Soc. Brasil. Mat. (N.S.), 1990, 21(1), 1–10. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 489–499.]
Arnold V. I. Dynamics of intersections. In: Analysis, et cetera. Research papers published in honor of Jürgen Moser's 60th birthday. Editors: P. H. Rabinowitz and E. Zehnder. Boston, MA: Academic Press, 1990, 77–84.
Arnold V. I. Bounds for Milnor numbers of intersections in holomorphic dynamical systems. In: Topological Methods in Modern Mathematics. Proceedings of the symposium in honor of John Milnor's sixtieth birthday (Stony Brook, NY, 1991). Editors: L. R. Goldberg and A. V. Phillips. Houston, TX: Publish or Perish, 1993, 379–390.
Gabrielov A. M., KhovanskiĬ A. G. Multiplicity of a Noetherian intersection. In: Geometry of Differential Equations. Editors: A. G. Khovanskiĭ, A. N. Varchenko and V. A. Vassiliev. Providence, RI: Amer. Math. Soc., 1998, 119–130. (AMS Transl., Ser. 2, 186; Adv. Math. Sci., 39.)
Novikov D. I., Yakovenko S. Yu. Trajectories of polynomial vector fields and ascending chains of polynomial ideals. Ann. Inst. Fourier (Grenoble), 1999, 49(2), 563–609.
Risler J.-J. A bound for the degree of nonholonomy in the plane. Theoret. Comput. Sci., 1996, 157(1), 129–136.
1971-11 — A. M. Lukatskiĭ
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
Chepyzhov V. V., Vishik M. I. A Hausdorff dimension estimate for kernel sections of nonautonomous evolution equations. Indiana Univ. Math. J., 1993, 42(3), 1057–1076.
Il'yashenko Yu. S. Weakly contracting systems and attractors of the Galerkin approximations of the Navier-Stokes equations on a two-dimensional torus. Uspekhi Mekhaniki, 1982, 5(1–2), 31–63 (in Russian). [The English translation: Selecta Math. Sov., 1992, 11(3), 203–239.]
Il'yashenko Yu. S. On the dimension of attractors of k-contracting systems in an infinite-dimensional space. Moscow Univ. Math. Bull., 1983, 38(3), 61–69.
Il'yashenko Yu. S., Chetaev A. N. On the dimension of attractors for a class of dissipative systems. J. Appl. Math. Mech., 1983, 46(3), 290–295.
Il'yin A. A. Partly dissipative semigroups generated by the Navier-Stokes system on two-dimensional manifolds, and their attractors. Sb. Math., 1994, 78(1), 47–76.
Il'yin A. A. Attractors for Navier-Stokes equations in domains with finite measure. Nonlinear Anal., 1996, 27(5), 605–616.
Ladyzhenskaya O. A. The finite-dimensionality of bounded invariant sets for the Navier-Stokes system and other dissipative systems. Zap. Nauch. Semin. Leningrad. Otd. Mat. Inst. Steklova, 1982, 115, 137–155 (in Russian). (Boundary Problems in Mathematical Physics and Related Questions of the Function Theory, 14.)
Témam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics. New York: Springer, 1988. (Appl. Math. Sci., 68.)
1972-2 — S. V. Chmutov
Gabrielov A. M. Intersection matrices for certain singularities. Funct. Anal. Appl., 1973, 7(3), 182–193.
Looijenga E. J. N. On the semi-universal deformation of a simple-elliptic hyper-surface singularity. II. The discriminant. Topology, 1978, 17(1), 23–40.
1972-3 — V. D. Sedykh
Arnold V. I. Lectures on bifurcations in versal families. Russian Math. Surveys, 1972, 27(5), 54–123.
Arnold V. I. Catastrophe Theory. Berlin: Springer, 1992, Sect. 10. [The Russian original 1990.]
Arnold V. I., Vassiliev V. A., Goryunov V. V., Lyashko O. V. Singularities. I. Local and Global Theory. Berlin: Springer, 1993, Sect. 3.3. (Encyclopædia Math. Sci., 6; Dynamical Systems, VI.) [The Russian original 1988.]
Arnold V. I., Gusein-Zade S. M., Varchenko A. N. Singularities of Differentiable Maps, Vol. I: The classification of critical points, caustics and wave fronts. Boston, MA: Birkhäuser, 1985, Sect. 10.3.5. (Monographs in Math., 82.) [The Russian original 1982.]
LevantovskiĬ L. V. Singularities of the boundary of the stability domain. Funct. Anal. Appl., 1982, 16(1), 34–37.
Matov V. I. The topological classification of germs of the maximum and minimax functions of a family of functions in general position. Russian Math. Surveys, 1982, 37(4), 127–128.
1972-5 — V. N. Karpushkin
Arnold V. I. Remarks on the stationary phase method and Coxeter numbers. Russian Math. Surveys, 1973, 28(5), 19–48.
Colin de Verdière Y. Nombre de points entiers dans une famille homothétique de domaines de \(\mathbb{R}^n \). Ann. Sci. École Norm. Sup., Sér. 4, 1977, 10(4), 559–575.
Duistermaat J. Oscillatory integrals, Lagrangian immersions and unfolding of singularities. Commun. Pure Appl. Math., 1974, 27(2), 209–281.
Karpushkin V. N. Uniform estimates of integrals with unimodal phase. Uspekhi Mat. Nauk, 1983, 38(3), 128 (in Russian).
Karpushkin V. N. Uniform estimates of oscillatory integrals with a parabolic or hyperbolic phase. Trudy Semin. Petrovskogo, 1983, 9, 1–39 (in Russian). [The English translation: J. Sov. Math., 1986, 33, 1159–1188.]
Karpushkin V. N. A theorem concerning uniform estimates of oscillatory integrals when the phase is a function of two variables. Trudy Semin. Petrovskogo, 1984, 10, 150–169 (in Russian). [The English translation: J. Sov. Math., 1986, 35, 2809–2826.]
Karpushkin V. N. Uniform estimates for oscillatory integrals and volumes under a partial deformation of a phase. In: Geometry and the Theory of Singularities in Nonlinear Equations. Voronezh: Voronezh University Press, 1987, 151–159 (in Russian). (Novoe v Global'nom Analize, 7.)
Karpushkin V. N. Uniform estimates for some oscillating integrals. Sib. Math. J., 1989, 30(2), 240–249.
Karpushkin V. N. Oscillatory integrals and volumes with semiquasihomogeneous phase. Funct. Anal. Appl., 1992, 26(1), 46–48.
Karpushkin V. N. Dominant term in the asymptotics of oscillatory integrals with a phase of the series T. Math. Notes, 1994, 56(6), 1304–1305.
Karpushkin V. N. A remark about uniform estimates and counterexample of A. N. Varchenko. In: Some Problems of Fundamental and Applied Mathematics. Moscow: Moscow Instintute of Physics and Technology Press, 1998, 74–79 (in Russian).
Karpushkin V. N. Uniform estimates of oscillatory integrals with phase from the series \(\tilde R_m \). Math. Notes, 1998, 64(3), 404–406.
Karpushkin V. N. Uniform estimates of volumes. Proc. Steklov Inst. Math., 1998, 221, 214–220.
Popov D. A. Estimates with constants for some classes of oscillatory integrals. Russian Math. Surveys, 1997, 52(1), 73–145.
Varchenko A. N. Newton polyhedra and estimation of oscillating integrals. Funct. Anal. Appl., 1976, 10(3), 175–196.
Vinogradov I. M. The Method of Trigonometric Sums in the Number Theory. Moscow: Nauka, 1971 (in Russian).
1972-6 — S. M. Gusein-Zade
Arnold V. I. Remarks on the stationary phase method and Coxeter numbers. Russian Math. Surveys, 1973, 28(5), 19–48.
Tyurina G. N. The topological properties of isolated singularities of complex spaces of codimension one. Math. USSR, Izv., 1968, 2, 557–571.
1972-7
Arnold V. I. Modes and quasimodes. Funct. Anal. Appl., 1972, 6(2), 94–101. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 189–202.]
1972-7 — Ya. M. Dymarskiĭ
DymarskiĬ Ya. M. On manifolds of self-adjoint elliptic operators with multiple eigenvalues. Methods Funct. Anal. Topology, 2001, 7(2), 68–74.
DymarskiĬ Ya. M. Manifolds of eigenfunctions and potentials of a family of periodic Sturm-Liouville problems. Ukrain. Math. J., 2002, 54(8), 1251–1264.
Lupo D., Micheletti A. M. On multiple eigenvalues of selfadjoint compact operators. J. Math. Anal. Appl., 1993, 172(1), 106–116.
Lupo D., Micheletti A. M. A remark on the structure of the set of perturbations which keep fixed the multiplicity of two eigenvalues. Revista Mat. Apl., 1995, 16(2), 47–56.
Lupo D., Micheletti A. M. On the persistence of the multiplicity of eigenvalues for some variational elliptic operator depending on the domain. J. Math. Anal. Appl., 1995, 193(3), 990–1002.
Uhlenbeck K. Generic properties of eigenfunctions. Amer. J. Math., 1976, 98(4), 1059–1078.
1972-8 — V. N. Karpushkin
Arnold V. I. Modes and quasimodes. Funct. Anal. Appl., 1972, 6(2), 94–101. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 189–202.]
Arnold V. I. Frequent representations. Moscow Math. J., 2003, 3(4), 14 pp.
Karpushkin V. N. On the asymptotic behavior of eigenvalues of symmetric manifolds and on most probable representations of finite groups. Moscow Univ. Math. Bull., 1974, 29(2), 136–139.
1972-9 — A. I. Neĭshtadt
Arnold V. I. Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd edition. New York: Springer, 1988. (Grundlehren der Mathematischen Wissenschaften, 250.) [The Russian original 1978.]
Arnold V. I., Kozlov V. V., NeĬshtadt A. I. Mathematical Aspects of Classical and Celestial Mechanics, 2nd edition. Berlin: Springer, 1993. (Encyclopædia Math. Sci., 3; Dynamical Systems, III.) [The Russian original 1985.] [The second, revised and supplemented, Russian edition 2002.]
Bakhtin V. I. Averaging method in multi-frequency systems. Ph. D. Thesis, Moscow State University, 1986 (in Russian).
Bakhtin V. I. Averaging in a general-position single-frequency system. Differ. Equations, 1991, 27(9), 1051–1061.
NeĬshtadt A. I. On some resonant problems in nonlinear systems. Ph. D. Thesis, Moscow State University, 1975 (in Russian).
NeĬshtadt A. I. Passage through a resonances in the two-frequency problem. Sov. Phys. Dokl., 1975, 20(3), 189–191.
NeĬshtadt A. I. Scattering by resonances. Celest. Mech. Dynam. Astron., 1996/97, 65(1–2), 1–20.
Pronchatov V. E. An error estimate for the averaging method in the two-frequency problem. Math. USSR, Sb., 1985, 50(1), 241–258.
Pronchatov V. E. On an error estimate for the averaging method in the two-frequency problem. Math. USSR, Sb., 1989, 62(1), 29–40.
1972-10 — A. I. Neĭshtadt
Arnold V. I. Conditions for the applicability and estimate of the error of an averaging method for systems which pass through the states of resonance in the course of their evolution. Sov. Math. Dokl., 1965, 6, 331–334. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 69–74.]
Anosov D. V. Averaging in systems of ordinary differential equations with rapidly oscillating solutions. Izv. Akad. Nauk SSSR, Ser. Mat., 1960, 24(5), 721–742 (in Russian).
Bakhtin V. I. Averaging in multi-frequency systems. Funct. Anal. Appl., 1986, 20(2), 83–88.
Dodson M. M., Rynne B. P., Vickers J. A. G. Averaging in multi-frequency systems. Nonlinearity, 1989, 2(1), 137–148.
Kasuga T. On the adiabatic theorem for the Hamiltonian system of differential equations in the classical mechanics, I; II; III. Proc. Japan. Acad., 1961, 37(7), 366–371; 372–376; 377–382.
NeĬshtadt A. I. Averaging in multi-frequency systems, II. Sov. Phys. Dokl., 1976, 21(2), 80–82.
1972-11 — V. A. Vassiliev
Goryunov V. V. Cohomology of braid groups of series C and D. Trans. Moscow Math. Soc., 1982, 42, 233–241.
Salvetti M. The homotopy tupe of Artin groups. Math. Res. Lett., 1994, 1(5), 565–577.
1972-12 — V. D. Sedykh
Bogaevsky I. A. Singularities of convex hulls of three-dimensional hypersurfaces. Proc. Steklov Inst. Math., 1998, 221, 71–90.
Kiselman C. O. How smooth is the shadow of a smooth convex body. J. London Math. Soc., Ser. 2, 1986, 33(1), 101–109; Serdica Math. J., 1986, 12(2), 189–195.
Sedykh V. D. Singularities of the convex hull of a curve in \(\mathbb{R}^3 \). Funct. Anal. Appl., 1977, 11(1), 72–73.
Sedykh V. D. Moduli of singularities of convex hulls. Russian Math. Surveys, 1981, 36(5), 175–176.
Sedykh V. D. Structure of the convex hull of a space curve. Trudy Semin. Petrovskogo, 1981, 6, 239–256 (in Russian). [The English translation: J. Sov. Math., 1986, 33, 1140–1153.]
Sedykh V. D. Singularities of convex hulls. Sib. Math. J., 1983, 24(3), 447–461.
Sedykh V. D. Convex hulls and the Legendre transform. Sib. Math. J., 1983, 24(6), 923–933.
Sedykh V. D. Functional moduli of singularities of convex hulls of manifolds of codimension 1 and 2. Math. USSR, Sb., 1984, 47(1), 223–236.
Sedykh V. D. Stabilization of singularities of convex hulls. Math. USSR, Sb., 1989, 63(2), 499–505.
Sedykh V. D. The sewing of a swallowtail and a Whitney umbrella in a four-dimensional controlled system. In: Proceedings of Gubkin State Oil and Gas Academy. Moscow: Neft’ i Gaz, 1997, 58–68 (in Russian).
Zakalyukin V. M. Singularities of convex hulls of smooth manifolds. Funct. Anal. Appl., 1978, 11(3), 225–227.
1972-13 — V. A. Vassiliev
Arnold V. I. Normal forms of functions in neighborhoods of degenerate critical points. Russian Math. Surveys, 1974, 29(2), 10–50.
Kushnirenko A. G. Polyèdres de Newton et nombres de Milnor. Invent. Math., 1976, 32(1), 1–31.
Varchenko A. N. A lower bound for the codimension of the stratum μ = const in terms of the mixed Hodge structure. Moscow Univ. Math. Bull., 1982, 37(6), 30–33.
1972-14 — V. V. Goryunov
Arnold V. I., Vassiliev V. A., Goryunov V. V., Lyashko O. V. Singularities. I. Local and Global Theory. Berlin: Springer, 1993, Ch. 2, Sect. 5. (Encyclopædia Math. Sci., 6; Dynamical Systems, VI.) [The Russian original 1989.]
Arnold V. I., Vassiliev V. A., Goryunov V. V., Lyashko O. V. Singularities. II. Classification and Applications. Berlin: Springer, 1993, Ch. 1. (Encyclopædia Math. Sci., 39; Dynamical Systems, VIII.) [The Russian original 1989.]
Goryunov V. V., Baines C. E. Cyclically equivariant function singularities and unitary reflection groups G(2m,2,n), G9 and G31. St. Petersburg Math. J., 2000, 11(5), 761–774.
Jaworski P. Distribution of critical values of miniversal deformations of parabolic singularities. Invent. Math., 1986, 86(1), 19–33.
Knörrer H. Zum K(π, 1)-Problem für isolierte Singularitäten von vollständigen Durchschnitten. Compos. Math., 1982, 45(3), 333–340.
Nakamura T. A note on the K(π, 1) property of the orbit space of the unitary reflection group G(m,l,n). Sci. Papers College Arts Sci. Univ. Tokyo, 1983, 33(1), 1–6.
Shephard G. C., Todd J. A. Finite unitary reflection groups. Canad. J. Math., 1954, 6, 274–304.
1972-14 — V. A. Vassiliev
Brieskorn E. Sur les groupes de tresses [d'après V. I. Arnold]. In: Séminaire Bourbaki, 24ème année (1971/1972), Exp. No. 401. Berlin: Springer, 1973, 21–44. (Lecture Notes in Math., 317.)
Deligne P. Les immeubles de groupes de tresses généralisés. Invent Math., 1972, 17, 273–302.
Goryunov V. V. Geometry of bifurcation diagrams of simple projections onto the line. Funct. Anal. Appl., 1981, 15(2), 77–82.
Goryunov V. V. Projection of 0-dimensional complete intersection onto a line and the K(π, 1)-conjecture. Russian Math. Surveys, 1982, 37(3), 206–208.
Goryunov V. V. Singularities of projections of complete intersectrions. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics, Vol. 22. Moscow: VINITI, 1983, 167–206 (in Russian). [The English translation: J. Sov. Math., 1984, 27, 2785–2811.]
Goryunov V. V. Vector fields and functions on the discriminants of complete intersections, and bifurcation diagrams of projections. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics. Newest Results, Vol. 33. Moscow: VINITI, 1988, 31–54 (in Russian). [The English translation: J. Sov. Math., 1990, 52(4), 3231–3245.]
Knörrer H. Zum K(π, 1)-Problem für isolierte Singularitäten von vollständigen Durchschnitten. Compos. Math., 1982, 45(3), 333–340.
Looijenga E. J. N. The complement of the bifurcation variety of a simple singularity. Invent. Math., 1974, 23(2), 105–116.
Lyashko O. V. The geometry of bifurcation diagrams. Russian Math. Surveys, 1979, 34(3), 209–210.
1972-16 — V. I. Arnold
Roytvarf A. A. The motion of a continuous medium in the force field with a rooted singularity. Moscow Univ. Mech. Bull., 1987, 42(1), 24–27.
Roytvarf A. A. Two-valued velocity field with a square root singularity. Moscow Univ. Mech. Bull., 1988, 43(3), 16–19.
Roytvarf A. A. On the dynamics of a one-dimensional self-gravitating medium. Physica D, 1994, 73(3), 189–204.
1972-17
Arnold V. I. A comment to H. Poincaré's paper “Sur un théorème de géométrie.” In: Poincaré H. Selected Works in Three Volumes (in Russian). Editors: N. N. Bogolyubov, V. I. Arnold and I. B. Pogrebysskiĭ. Vol. II. New methods of celestial mechanics. Topology. Number theory. Moscow: Nauka, 1972, 987–989 (in Russian).
Arnold V. I. Sur une propriété topologique des applications globalement canoniques de la mécanique classique. C. R. Acad. Sci. Paris, 1965, 261(19), 3719–3722.
The Russian translation in: [2b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 81–86.
1972-18
Arnold V. I. A comment to H. Poincaré's paper “Sur un théorème de géométrie.” In: Poincaré H. Selected Works in Three Volumes (in Russian). Editors: N. N. Bogolyubov, V. I. Arnold and I. B. Pogrebysskiĭ. Vol. II. New methods of celestial mechanics. Topology. Number theory. Moscow: Nauka, 1972, 987–989 (in Russian).
1972-20 — A. A. Glutsyuk, M. B. Sevryuk
Arnold V. I. On mappings of the circle onto itself. Diploma Thesis, Faculty of Mechanics and Mathematics of Moscow State University, 1959 (in Russian).
Arnold V. I. On analytic mappings of the circle onto itself. Uspekhi Mat. Nauk, 1960, 15(2), 212–214 (in Russian).
Arnold V. I. Small denominators I. Mappings of the circumference onto itself. Izv. Akad. Nauk SSSR, Ser. Mat., 1961, 25(1), 21–86; corrigenda: 1964, 28(2), 479–480 (in Russian). [The English translation: AMS Transl., Ser. 2, 1965, 46, 213–284.]
Arnold V. I. Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd edition. New York: Springer, 1988, §§ 11–12. (Grundlehren der Mathematischen Wissenschaften, 250.) [The Russian original 1978.]
Arnold V. I. Sur quelques problèmes de la théorie des systèmes dynamiques. Topol. Methods Nonlinear Anal., 1994, 4(2), 209–225. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 533–551.]
Arnold V. I. From Hilbert's superposition problem to dynamical systems. In: The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (Toronto, 1997). Editors: E. Bierstone, B. A. Khesin, A. G. Khovanskiĭ and J. E. Marsden. Providence, RI: Amer. Math. Soc., 1999, 1–18. (Fields Institute Commun., 24.) [The Russian version in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 727–740.]
Herman M. R. Conjugaison C∞ des difféomorphismes du cercle dont le nombre de rotations satisfait à une condition arithmétique. C. R. Acad. Sci. Paris, Sér. A–B, 1976, 282(10), Ai, A503–A506.
Herman M. R. Conjugaison C∞ des difféomorphismes du cercle pour presque tout nombre de rotation. C. R. Acad. Sci. Paris, Sér. A–B, 1976, 283(8), Aii, A579–A582.
Herman M. R. La conjugaison des difféomorphismes du cercle à des rotations. Bull. Soc. Math. France Suppl. Mém., 1976, 46, 181–188 [Supplément au Bull. Soc. Math. France, 1976, 104(2)].
Herman M. R. Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. Thèse d'État, Univ. Paris-Sud, Orsay, 1976.
Herman M. R. Mesure de Lebesgue et nombre de rotation. In: Geometry and Topology. Proc. III Latin Amer. School of Math. (Rio de Janeiro, 1976). Editors: J. Palis and M. do Carmo. Berlin: Springer, 1977, 271–293. (Lecture Notes in Math., 597.)
Herman M. R. Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. Inst. Hautes Études Sci. Publ. Math., 1979, 49, 5–233.
Herman M. R. Résultats récents sur la conjugaison différentiable. In: Proceedings of the International Congress of Mathematicians (Helsinki, 1978), Vol. 2. Editor: O. Lehto. Helsinki: Acad. Sci. Fennica, 1980, 811–820.
Herman M. R. Sur les difféomorphismes du cercle de nombre de rotation de type constant. In: Conference on Harmonic Analysis in Honor of Antoni Zygmund (Chicago, 1981), Vol. II. Editors: W. Beckman, A. P. Calderón, R. Fefferman and P. W. Jones. Belmont: Wadsworth, 1983, 708–725.
Herman M. R. Simple proofs of local conjugacy theorems for diffeomorphisms of the circle with almost every rotation number. Bol. Soc. Brasil. Mat. (N. S.), 1985, 16(1), 45–83.
Herman M. R. Recent results and some open questions on Siegel's linearization theorem of germs of complex analytic diffeomorphisms of \(\mathbb{C}^n \) near a fixed point. In: VIIIth Intern. Congress on Mathematical Physics (Marseille, 1986). Editors: M. Mebkhout and R. Sénéor. Singapore: World Scientific, 1987, 138–184.
Katznelson Y., Ornstein D. S. The differentiability of the conjugation of certain diffeomorphisms of the circle. Ergod. Theory Dynam. Systems, 1989, 9(4), 643–680.
Katznelson Y., Ornstein D. S. The absolute continuity of the conjugation of certain diffeomorphisms of the circle. Ergod. Theory Dynam. Systems, 1989, 9(4), 681–690.
Khanin K. M., SinaĬ Ya. G. A new proof of M. Herman's theorem. Commun. Math. Phys., 1987, 112(1), 89–101.
Pérez-Marco R. Sur la structure des germes holomorphes non linéarisables. C. R. Acad. Sci. Paris, Sér. I Math., 1991, 312(7), 533–536.
Pérez-Marco R. Centralisateurs non dénombrables de germes de difféomorphismes holomorphes non linéarisables de (\(\mathbb{C}\), 0). C. R. Acad. Sci. Paris, Sér. I Math., 1991, 313(7), 461–464.
Pérez-Marco R. Solution complète au problème de Siegel de linéarisation d'une application holomorphe au voisinage d'un point fixe (d'après J.-C. Yoccoz). In: Séminaire Bourbaki, 1991–92; Astérisque, 1992, 206, Exp. No. 753, 4, 273–310.
Pérez-Marco R. Sur les dynamiques holomorphes non linéarisables et une conjecture de V. I. Arnold. Ann. Sci. École Norm. Sup., Sér. 4, 1993, 26(5), 565–644.
Pérez-Marco R. Nonlinearizable holomorphic dynamics having an uncountable number of symmetries. Invent. Math., 1995, 119(1), 67–127.
Pérez-Marco R. Fixed points and circle maps. Acta Math., 1997, 179(2), 243–294.
Pérez-Marco R. Siegel disks with quasi-analytic boundary. Preprint, Université Paris-Sud.
Pérez-Marco R. Total convergence or general divergence in small divisors. Commun. Math. Phys., 2001, 223(3), 451–464.
SinaĬ Ya. G., Khanin K. M. Smoothness of conjugacies of diffeomorphisms of the circle with rotations. Russian Math. Surveys, 1989, 44(1), 69–99.
Stark J. Smooth conjugacy and renormalisation for diffeomorphisms of the circle. Nonlinearity, 1988, 1(4), 541–575.
Yoccoz J.-C. Centralisateur d'un difféomorphisme du cercle dont le nombre de rotation est irrationnel. C. R. Acad. Sci. Paris, Sér. A–B, 1980, 291(9), A523–A526.
Yoccoz J.-C.C1-conjugaison des difféomorphismes du cercle. In: Geometric Dynamics. Proc. Intern. Symp. at the IMPA (Rio de Janeiro, 1981). Editor: J. Palis, Jr. Berlin: Springer, 1983, 814–827. (Lecture Notes in Math., 1007.)
Yoccoz J.-C. Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne. Ann. Sci. École Norm. Sup., Sér. 4, 1984, 17(3), 333–359.
Yoccoz J.-C. Il n'y a pas de contre-exemple de Denjoy analytique. C. R. Acad. Sci. Paris, Sér. I Math., 1984, 298(7), 141–144.
Yoccoz J.-C. Centralisateurs et conjugaison différentiable des difféomorphismes du cercle. Thèse d'État, Univ. Paris-Sud, Orsay, 1985.
Yoccoz J.-C. Linéarisation des germes de difféomorphismes holomorphes de (\(\mathbb{C}\), 0). C. R. Acad. Sci. Paris, Sér. I Math., 1988, 306(1), 55–58.
Yoccoz J.-C. Théorème de Siegel, nombres de Bruno et polynômes quadratiques. In: Petits Diviseurs en Dimension 1. Astérisque, 1995, 231, 3–88.
Yoccoz J.-C. Centralisateurs et conjugaison différentiable des difféomorphismes du cercle. In: Petits Diviseurs en Dimension 1. Astérisque, 1995, 231, 89–242.
1972-21 — M. B. Sevryuk
Adrianova L. Ya. On reducibility of systems of n linear differential equations with quasi-periodic coefficients. Vestnik Leningrad. Univ., Ser. Mat., Mekh., Astron., 1962, 7(2), 14–24 (in Russian).
Arnold V. I. Small denominators and problems of stability of motion in classical and celestial mechanics. Russian Math. Surveys, 1963, 18(6), 85–191 (see Ch. VI, § 2, no 5).
Arnold V. I. Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd edition. New York: Springer, 1988, § 26. (Grundlehren der Mathematischen Wissenschaften, 250.) [The Russian original 1978.]
Bogolyubov N. N., Mitropol'skiĬ Yu. A., SamoĬlenko A. M. Methods of Accelerated Convergence in Nonlinear Mechanics. New York: Springer, 1976, Ch. V. [The Russian original 1969.]
Broer H. W., Huitema G. B., Sevryuk M. B. Quasi-Periodic Motions in Families of Dynamical Systems: Order amidst Chaos. Berlin: Springer, 1996, Sect. 1.5. (Lecture Notes in Math., 1645.)
BronshteĬn I. U., CherniĬ V. F. Linear extensions satisfying the Perron condition. I; II. Differ. Equations, 1978, 14(10), 1234–1243; 1980, 16(2), 123–128.
Bylov B. F., Vinograd R. E., Grobman D. M., NemytskiĬ V. V. The Theory of Lyapunov Exponents and Its Applications to Stability Problems. Moscow: Nauka, 1966, Ch. VII (in Russian).
Bylov B. F., Vinograd R. E., Lin V. Ya., LokutsievskiĬ O. V. On topological obstacles to block diagonalization for some exponentially split almost periodic systems. Preprint of the Moscow Institute for Applied Mathematics, the USSR Academy of Sciences, 1977, № 58 (in Russian).
Bylov B. F., Vinograd R. E., Lin V. Ya., LokutsievskiĬ O. V. On topological reasons for anomalous behavior of some almost periodic systems. In: Problems of Asymptotic Theory of Nonlinear Oscillations. Editors: N. N. Bogolyubov, A. Yu. Ishlinskiĭ, V. S. Korolyuk, O. B. Lykova, A. M. Samoĭlenko and A. N. Sharkovskiĭ. Kiev: Naukova Dumka, 1977, 54–61 (in Russian).
Dinaburg E. I., SinaĬ Ya. G. On the one-dimensional Schrödinger equation with a quasi-periodic potential. Funct. Anal. Appl., 1975, 9(4), 279–289.
Eliasson L. H. Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation. Commun. Math. Phys., 1992, 146(3), 447–482.
Eliasson L. H. Reducibility and point spectrum for linear quasi-periodic skew-products. In: Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998). Doc. Math., 1998, Extra Vol. II, 779–787 (electronic).
Eliasson L. H. On the discrete one-dimensional quasi-periodic Schrödinger equation and other smooth quasi-periodic skew products. In: Hamiltonian Systems with Three or More Degrees of Freedom (S'Agaró, 1995). Editor: C. Simó. Dordrecht: Kluwer Acad. Publ., 1999, 55–61. (NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 533.)
Eliasson L. H. Almost reducibility of linear quasi-periodic systems. In: Smooth Ergodic Theory and Its Applications. Proc. AMS Summer Research Inst. (Seattle, WA, 1999). Editors: A. B. Katok, R. de la Llave, Ya. B. Pesin and H. Weiss. Providence, RI: Amer. Math. Soc., 2001, 679–705. (Proc. Symposia Pure Math., 69.)
Gel'man A. E. On reducibility of a certain class of systems of differential equations with quasi-periodic coefficients. Dokl. Akad. Nauk SSSR, 1957, 116(4), 535–537 (in Russian).
Herman M. R. Construction d'un difféomorphisme minimal d'entropie topologique non nulle. Ergod. Theory Dynam. Systems, 1981, 1(1), 65–76.
Herman M. R. Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2. Comment. Math. Helvetici, 1983, 58(3), 453–502.
Johnson R. A., Sell G. R. Smoothness of spectral subbundles and reducibility of quasi-periodic linear differential systems. J. Differ. Equations, 1981, 41(2), 262–288.
Jorba À. Numerical computation of the normal behaviour of invariant curves of n-dimensional maps. Nonlinearity, 2001, 14(5), 943–976.
Jorba À., Ramírez-Ros R., Villanueva J. Effective reducibility of quasiperiodic linear equations close to constant coefficients. SIAM J. Math. Anal., 1997, 28(1), 178–188.
Jorba À., Simó C. On the reducibility of linear differential equations with quasiperiodic coefficients. J. Differ. Equations, 1992, 98(1), 111–124.
Jorba À., Simó C. On quasiperiodic perturbations of elliptic equilibrium points. SIAM J. Math. Anal., 1996, 27(6), 1704–1737.
Krikorian R. Réductibilité presque partout des systèmes quasi périodiques analytiques dans le cas SO(3). C. R. Acad. Sci. Paris, Sér. I Math., 1995, 321(8), 1039–1044.
Krikorian R.C0-densité globale des systèmes produits-croisés sur le cercle réductibles. Ergod. Theory Dynam. Systems, 1999, 19(1), 61–100.
Krikorian R. Réductibilité des Systémes Produits-Croisés à Valeurs dans des Groupes Compacts. Paris: Soc. Math. France, 1999. (Astérisque, 259.)
Krikorian R. Réductibilité presque partout des flots fibrés quasi-périodiques à valeurs dans des groupes compacts. Ann. Sci. École Norm. Sup., Sér. 4, 1999, 32(2), 187–240.
Kuksin S. B. An infinitesimal Liouville-Arnold theorem as a criterion of reducibility for variational Hamiltonian equations. Chaos, Solitons & Fractals, 1992, 2(3), 259–269.
Millionshchikov V. M. A proof of the existence of non-regular systems of linear differential equations with quasi-periodic coefficients. Differ. Uravneniya, 1969, 5(11), 1979–1983 (in Russian, for the English translation see Differ. Equations).
Millionshchikov V. M. On typicality of almost reducible systems with almost periodic coefficients. Differ. Equations, 1978, 14(4), 448–450.
Moser J., Pöschel J. An extension of a result by Dinaburg and Sinaĭ on quasiperiodic potentials. Comment. Math. Helvetici, 1984, 59(1), 39–85.
Moshchevitin N. G. Recent results on asymptotic behavior of integrals of quasiperiodic functions. In: Dynamical Systems in Classical Mechanics. Editor: V. V. Kozlov. Providence, RI: Amer. Math. Soc., 1995, 201–209. (AMS Transl., Ser. 2, 168; Adv. Math. Sci., 25.)
Moshchevitin N. G. Multidimensional Diophantine approximations and dynamical systems. Reg. Khaot. Dinamika, 1997, 2(1), 81–95 (in Russian).
Moshchevitin N. G. Differential equations with almost periodic and conditionally periodic coefficients: recurrence and reducibility. Math. Notes, 1998, 64(1–2), 194–201.
Sprindžuk V. G. Quasi-periodic functions with the unbounded indefinite integral. Dokl. Akad. Nauk Beloruss. SSR, 1968, 12(1), 5–9 (in Russian).
Treshchëv D. V. An estimate of irremovable nonconstant terms in the reducibility problem. In: Dynamical Systems in Classical Mechanics. Editor: V. V. Kozlov. Providence, RI: Amer. Math. Soc., 1995, 91–128. (AMS Transl., Ser. 2, 168; Adv. Math. Sci., 25.)
Treshchëv D. V. On the reducibility of the one-dimensional Schrödinger equation with quasi-periodic potential. In: Dynamical Systems in Classical Mechanics. Editor: V. V. Kozlov. Providence, RI: Amer. Math. Soc., 1995, 129–140. (AMS Transl., Ser. 2, 168; Adv. Math. Sci., 25.)
Wagener F. O. O. On the skew Hopf bifurcation. Ph. D. Thesis, University of Groningen, 1998.
1972-22 — M. B. Sevryuk
Beresnevich V. V., Bernik V. I. Extremal smooth curves in the three-dimensional Euclidean space. Dokl. Akad. Nauk Belarusi, 1994, 38(3), 9–12 (in Russian).
Beresnevich V. V., Bernik V. I. On a metrical theorem of W. Schmidt. Acta Arithm., 1996, 75(3), 219–233.
Bernik V. I., Dodson M. M. Metric Diophantine Approximation on Manifolds. Cambridge: Cambridge University Press, 1999. (Cambridge Tracts in Math., 137.)
Bernik V. I., Kovalevskaya E. I. Diophantine approximations on manifolds of dimension n in \(\mathbb{R}^{2n} \). Dokl. Akad. Nauk Beloruss. SSR, 1990, 34(12), 1061–1064 (in Russian).
Dodson M. M., Rynne B. P., Vickers J. A. G. Metric Diophantine approximation and Hausdorff dimension on manifolds. Math. Proc. Cambridge Phil. Soc., 1989, 105(3), 547–558.
Dodson M. M., Rynne B. P., Vickers J. A. G. Khintchine-type theorems on manifolds. Acta Arithm., 1991, 57(2), 115–130.
Kleinbock D. Ya. Some applications of homogeneous dynamics to number theory. In: Smooth Ergodic Theory and Its Applications. Proc. AMS Summer Research Inst. (Seattle, WA, 1999). Editors: A. B. Katok, R. de la Llave, Ya. B. Pesin and H. Weiss. Providence, RI: Amer. Math. Soc., 2001, 639–660. (Proc. Symposia Pure Math., 69.)
Kleinbock D. Ya., Margulis G. A. Flows on homogeneous spaces and Diophantine approximation on manifolds. Ann. Math., Ser. 2, 1998, 148(1), 339–360.
Pyartli A. S. Diophantine approximations on submanifolds of the Euclidean space. Funct. Anal. Appl., 1969, 3(4), 303–306.
Schmidt W. M. Metrische Sätze über simultane Approximation abhängiger Großen. Monatsh. Math., 1964, 68(2), 154–166.
Sprindžuk V. G. A proof of Mahler's conjecture on the measure of the set of S-numbers. Izvestiya Akad. Nauk SSSR, Ser. Matem., 1965, 29(2), 379–436 (in Russian).
Sprindžuk V. G. Mahler's Problem in Metric Number Theory. Providence, RI: Amer. Math. Soc., 1969. (Transl. Math. Monographs, 25.) [The Russian original 1967.]
Sprindžuk V. G. The method of trigonometric sums in the metric theory of Diophantine approximations of dependent quantities. Trudy Matem. Inst. im. V. A. Steklova, 1972, 128(2), 212–228 (in Russian, for the English translation see Proc. Steklov Inst. Math.).
Sprindžuk V. G. Metric Theory of Diophantine Approximations. New York: John Wiley, 1979. [The Russian original 1977.]
Sprindžuk V. G. Achievements and problems in the theory of Diophantine approximations. Russian Math. Surveys, 1980, 35(4), 1–80.
Starkov A. N. Dynamical Systems on Homogeneous Spaces. Providence, RI: Amer. Math. Soc., 2000. (Transl. Math. Monographs, 190.) [The Russian original 1999.]
1972-23 — A. A. Glutsyuk
Kurdyka K. On the gradient conjecture of R. Thom. In: Seminari di Geometria. 1998–1999 (Bologna, 1997). Editor: S. Coen. Bologna: Univ. Studi Bologna, 2000, 143–151.
Kurdyka K., Mostowski T., Parusiński A. Proof of the gradient conjecture of R. Thom. Ann. Math., Ser. 2, 2000, 152(3), 763–792.
Moussu R. Sur la dynamique des gradients. Existence de variétés invariantes. Math. Ann., 1997, 307(3), 445–460.
Thom R. Problèmes rencontrés dans mon parcours mathématique: un bilan. Inst. Hautes Études Sci. Publ. Math., 1989, 70, 199–214.
1972-23 — D. I. Novikov
Kurdyka K., Mostowski T. Parusiński A. Proof of the gradient conjecture of R. Thom. Ann. Math., Ser. 2, 2000, 152(3), 763–792.
1972-26 — V. M. Kharlamov
Arnold V. I., OleĬnik O. A. Topology of real algebraic varieties. Moscow Univ. Math. Bull., 1979, 34(6), 5–17.
Degtyarev A., Kharlamov V. Topological properties of real algebraic varieties: Rokhlin's way. Russian Math. Surveys, 2000, 55(4), 735–814.
Gudkov D. A. The topology of real projective algebraic varieties. Russian Math. Surveys, 1974, 29(4), 1–79.
Viro O. Ya. Progress in the topology of real algebraic varieties over the last six years. Russian Math. Surveys, 1986, 41(3), 55–82.
Wilson G. Hilbert's sixteenth problem. Topology, 1978, 17(1), 53–73.
1972-27 — F. Napolitano
Arnold V. I. On some topological invariants of algebraic functions. Trans. Moscow Math. Soc., 1970, 21, 30–52.
Arnold V. I. Cohomology classes of algebraic functions invariant under Tschirnhausen transformations. Funct. Anal. Appl., 1970, 4(1), 74–75. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 151–154.]
Arnold V. I. Topological invariants of algebraic functions, II. Funct. Anal. Appl., 1970, 4(2), 91–98.
Arnold V. I. From Hilbert's superposition problem to dynamical systems. In: The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (Toronto, 1997). Editors: E. Bierstone, B. A. Khesin, A. G. Khovanskiĭ and J. E. Marsden. Providence, RI: Amer. Math. Soc., 1999, 1–18. (Fields Inst. Commun., 24.)
Lin V. Ya. On superpositions of algebraic functions. Funct. Anal. Appl., 1972, 6(3), 240–241.
Lin V. Ya. Superpositions of algebraic functions. Funct. Anal. Appl., 1976, 10(1), 32–38.
1972-33
Arnold V. I. A comment to H. Poincaré's paper “Sur un théorème de géométrie.” In: Poincaré H. Selected Works in Three Volumes (in Russian). Editors: N. N. Bogolyubov, V. I. Arnold and I. B. Pogrebysskiĭ. Vol. II. New methods of celestial mechanics. Topology. Number theory. Moscow: Nauka, 1972, 987–989 (in Russian).
1972-33 — M. B. Sevryuk
Arnold V. I. Sur une propriété topologique des applications globalement canoniques de la mécanique classique. C. R. Acad. Sci. Paris, 1965, 261(19), 3719–3722. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 81–86.]
Arnold V. I. The stability problem and ergodic properties of classical dynamical systems. In: Proceedings of the International Congress of Mathematicians (Moscow, 1966). Moscow: Mir, 1968, 387–392 (in Russian). [The English translation: AMS Transl., Ser. 2, 1968, 70, 5–11.] [The original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 95–101.]
Arnold V. I. A comment to H. Poincaré's paper “Sur un théorème de géométrie.” In: Poincaré H. Selected Works in Three Volumes (in Russian). Editors: N. N. Bogolyubov, V. I. Arnold and I. B. Pogrebysskiĭ. Vol. II. New methods of celestial mechanics. Topology. Number theory. Moscow: Nauka, 1972, 987–989 (in Russian).
Arnold V. I. Fixed points of symplectic diffeomorphisms. In: Problems of present day mathematics. Editor: F. E. Browder. In: Mathematical Developments Arising from Hilbert Problems (Northern Illinois University, 1974). Part 1. Editor: F. E. Browder. Providence, RI: Amer. Math. Soc., 1976, 35–79; see XX, p. 66. (Proc. Symposia Pure Math., 28.)
Arnold V. I. Some problems in the theory of differential equations. In: Unsolved Problems of Mechanics and Applied Mathematics. Moscow: Moscow University Press, 1977, 3–9 (in Russian).
Arnold V. I. The first steps of symplectic topology. Russian Math. Surveys, 1986, 41(6), 1–21. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 365–389.]
Arnold V. I. First steps of symplectic topology. In: VIIIth Intern. Congress on Mathematical Physics (Marseille, 1986). Editors: M. Mebkhout and R. Sénéor. Singapore: World Scientific, 1987, 1–16.
Arnold V. I. On some problems in symplectic topology. In: Topology and Geometry. Rohlin Seminar. Editor: O. Ya. Viro. Berlin: Springer, 1988, 1–5. (Lecture Notes in Math., 1346.) [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 425–429.]
Arnold V. I. Mathematical Methods of Classical Mechanics, 2nd edition. New York: Springer, 1989, Appendix 9. (Graduate Texts in Math., 60.) [The Russian original 1974.]
Arnold V. I. Topological Invariants of Plane Curves and Caustics. Dean Jacqueline B. Lewis Memorial Lectures, Rutgers University. Providence, RI: Amer. Math. Soc., 1994. (University Lecture Series, 5.)
Arnold V. I. Symplectic geometry and topology. J. Math. Phys., 2000, 41(6), 3307–3343.
Chaperon M. Quelques questions de géométrie symplectique (d'après, entre autres, Poincaré, Arnold, Conley et Zehnder). In: Séminaire Bourbaki, 1982–83; Astérisque, 1983, 105–106, 231–249.
Chaperon M. Une idée du type “géodésiques brisées” pour les systèmes hamiltoniens. C. R. Acad. Sci. Paris, Sér. I Math., 1984, 298(13), 293–296.
Chaperon M. An elementary proof of the Conley-Zehnder theorem in symplectic geometry. In: Dynamical Systems and Bifurcations. Proc. Intern. Workshop at the Groningen University (Groningen, 1984). Editors: B. L. J. Braaksma, H. W. Broer and F. Takens. Berlin: Springer, 1985, 1–8. (Lecture Notes in Math., 1125.)
Chaperon M. Questions de géométrie symplectique. In: Géométrie Symplectique et Mécanique (Balaruc, 1983). Editor: J.-P. Dufour. Travaux en Cours. Paris: Hermann, 1985, 30–45.
Chaperon M., Zehnder E. Quelques résultats globaux en géométrie symplectique. In: Séminaire Sud-Rhodanien de Géométrie. III (Lyon, 1983). Géométrie Symplectique et de Contact: autour du Théorème de Poincaré-Birkhoff. Editors: P. Dazord and N. Desolneux-Moulis. Travaux en Cours. Paris: Hermann, 1984, 51–121.
Chekanov Yu. V. Legendrian Morse theory. Uspekhi Mat. Nauk, 1987, 42(4), 139 (in Russian).
Chekanov Yu. V. Critical points of quasifunctions, and generating families of Legendrian manifolds. Funct. Anal. Appl., 1996, 30(2), 118–128.
Chekanov Yu. V. Hofer's symplectic energy and Lagrangian intersections. In: Contact and Symplectic Geometry (Cambridge, 1994). Editor: C. B. Thomas. Cambridge: Cambridge University Press, 1996, 296–306. (Publ. Newton Inst., 8.)
Chekanov Ya. V. Lagrangian intersections, symplectic energy, and areas of holomorphic curves. Duke Math. J., 1998, 95(1), 213–226.
Conley C. C., Zehnder E. The Birkhoff-Lewis fixed point theorem and a conjecture of V. I. Arnold. Invent. Math., 1983, 73(1), 33–49.
Conley C. C., Zehnder E. A global fixed point theorem for symplectic maps and subharmonic solutions of Hamiltonian equations on tori. In: Nonlinear Functional Analysis and its Applications (University of California, 1983). Part 1. Editor: F. E. Browder. Providence, RI: Amer. Math. Soc., 1986, 283–299. (Proc. Symposia Pure Math., 45.)
Eliashberg Ya. M. Estimates of the number of fixed points of area-preserving transformations. Deposited in VINITI on January 30, 1979, № 374-79, 104 p. (in Russian), see also Ref. Zh. Mat., 1979, 5A491 (in Russian).
Eliashberg Ya. M., Gromov M. L. Lagrangian intersections and the stable Morse theory. Boll. Un. Mat. Ital. B, Ser. 7, 1997, 11(2), suppl., 289–326.
Eliashberg Ya. M., Gromov M. L. Lagrangian intersection theory: finite-dimensional approach. In: Geometry of Differential Equations. Editors: A. G. Khovanskiĭ, A. N. Varchenko and V. A. Vassiliev. Providence, RI: Amer. Math. Soc., 1998, 27–118. (AMS Transl., Ser. 2, 186; Adv. Math. Sci., 39.)
Floer A. Proof of the Arnold conjecture for surfaces and generalizations to certain Kähler manifolds. Duke Math. J., 1986, 53(1), 1–32.
Floer A. Holomorphic curves and a Morse theory for fixed points of exact symplectomorphisms. In: Séminaire Sud-Rhodanien de Géométrie. VI (Lyon, 1986). Aspects Dynamiques et Topologiques des Groupes Infinis de Transformation de la Mécanique. Editors: P. Dazord, N. Desolneux-Moulis and J.-M. Morvan. Travaux en Cours, 25. Paris: Hermann, 1987, 49–60.
Floer A. Morse theory for fixed points of symplectic diffeomorphisms. Bull. Amer. Math. Soc. (N. S.), 1987, 16(2), 279–281.
Floer A. An instanton-invariant for 3-manifolds. Commun. Math. Phys., 1988, 118(2), 215–240.
Floer A. Morse theory for Lagrangian intersections. J. Differ. Geom., 1988, 28(3), 513–547.
Floer A. Symplectic fixed points and holomorphic spheres. Commun. Math. Phys., 1989, 120(4), 575–611.
Floer A. Cuplength estimates on Lagrangian intersections. Commun. Pure Appl. Math., 1989, 42(4), 335–356.
Floer A., Zehnder E. Fixed point results for symplectic maps related to the Arnold conjecture. In: Dynamical Systems and Bifurcations. Proc. Intern. Workshop at the Groningen University (Groningen, 1984). Editors: B. L. J. Braaksma, H. W. Broer and F. Takens. Berlin: Springer, 1985, 47–63. (Lecture Notes in Math., 1125.)
Fortune B. A symplectic fixed point theorem for ℂPn. Invent. Math., 1985, 81(1), 29–46.
Fortune B., Weinstein A. A symplectic fixed point theorem for complex projective spaces. Bull. Amer. Math. Soc. (N. S.), 1985, 12(1), 128–130.
Fukaya K., Ono K. Arnold conjecture and Gromov-Witten invariant. Topology, 1999, 38(5), 933–1048.
Fukaya K., Ono K. Arnold conjecture and Gromov-Witten invariant for general symplectic manifolds. In: The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (Toronto, 1997). Editors: E. Bierstone, B. A. Khesin, A. G. Khovanskiĭ and J. E. Marsden. Providence, RI: Amer. Math. Soc., 1999, 173–190. (Fields Institute Commun., 24.)
Givental A. B. A symplectic fixed point theorem for toric manifolds. In: The Floer Memorial Volume. Editors: H. Hofer, C. H. Taubes, A. Weinstein and E. Zehnder. Basel: Birkhäuser, 1995, 445–481. (Progr. Math., 133.)
Gromov M. L. Pseudo holomorphic curves in symplectic manifolds. Invent. Math., 1985, 82(2), 307–347.
Hofer H. Lagrangian embeddings and critical point theory. Ann. Institut Henri Poincaré, Analyse non linéaire, 1985, 2(6), 407–462.
Hofer H. Ljusternik-Schnirelman theory for Lagrangian intersections. Ann. Institut Henri Poincaré, Analyse non linéaire, 1988, 5(5), 465–499.
Hofer H., Salamon D. A. Floer homology and Novikov rings. In: The Floer Memorial Volume. Editors: H. Hofer, C. H. Taubes, A. Weinstein and E. Zehnder. Basel: Birkhäuser, 1995, 483–524. (Progr. Math., 133.)
Hofer H., Zehnder E. Symplectic Invariants and Hamiltonian Dynamics. Basel: Birkhäuser, 1994, Ch. 6.
Ibort L. A., Martínez Ontalba C. Arnold's conjecture and symplectic reduction. J. Geom. Phys., 1996, 18(1), 25–37.
Laudenbach F., Sikorav J.-C. Persistance d'intersection avec la section nulle au cours d'une isotopie hamiltonienne dans un fibré cotangent. Invent. Math., 1985, 82(2), 349–357.
Lê H. V., Ono K. Symplectic fixed points, the Calabi invariant and Novikov homology. Topology, 1995, 34(1), 155–176.
Lê H. V., Ono K. Cup-length estimates for symplectic fixed points. In: Contact and Symplectic Geometry (Cambridge, 1994). Editor: C. B. Thomas. Cambridge: Cambridge University Press, 1996, 268–295. (Publ. Newton Inst., 8.)
Li J., Tian G. Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds. In: Topics in Symplectic 4-Manifolds (Irvine, CA, 1996). Editor: R. J. Stern. Cambridge, MA: Intern. Press, 1998, 47–83. (First Intern. Press Lecture Series, 1.)
Li J., Tian G. Comparison of algebraic and symplectic Gromov-Witten invariants. Asian J. Math., 1999, 3(3), 689–728.
Liu G., Tian G. Floer homology and Arnold conjecture. J. Differ. Geom., 1998, 49(1), 1–74.
Lu G. C. Arnold conjecture for product of monotone manifolds. Adv. Math. (China), 1993, 22(5), 463–465.
Lu G. C. The Arnold conjecture for a product of weakly monotone manifolds. Chinese J. Math., 1996, 24(2), 145–157.
Lu G. C. The Arnold conjecture for a product of monotone manifolds and Calabi-Yau manifolds. Acta Math. Sinica (N. S.), 1997, 13(3), 381–388.
McCord C., Oprea J. Rational Ljusternik-Schnirelmann category and the Arnold conjecture for nilmanifolds. Topology, 1993, 32(4), 701–717.
McDuff D., Salamon D. A. Introduction to Symplectic Topology, 2nd edition. New York: Clarendon Press, Oxford University Press, 1998, Ch. 11.
Oh Y.-G. A symplectic fixed point theorem on \(\mathbb{T}^{2n} \) × ℂPK. Math. Z., 1990, 203(4), 535–552.
Oh Y.-G. Floer cohomology and Arnold-Givental's conjecture on Lagrangian intersections. C. R. Acad. Sci. Paris, Sér. I Math., 1992, 315(3), 309–314.
Oh Y.-G. Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks. I. Commun. Pure Appl. Math., 1993, 46(7), 949–993; addendum: 1995, 48(11), 1299–1302.
Oh Y.-G. Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks. II. (ℂPn, \(\mathbb{R}{\text{P}}^n \)). Commun. Pure Appl. Math., 1993, 46(7), 995–1012.
Oh Y.-G. Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks. III. Arnold-Givental conjecture. In: The Floer Memorial Volume. Editors: H. Hofer, C. H. Taubes, A. Weinstein and E. Zehnder. Basel: Birkhäuser, 1995, 555–573. (Progr. Math., 133.)
Oh Y.-G. Relative Floer and quantum cohomology and the symplectic topology of Lagrangian submanifolds. In: Contact and Symplectic Geometry (Cambridge, 1994). Editor: C. B. Thomas. Cambridge: Cambridge University Press, 1996, 201–267. (Publ. Newton Inst., 8.)
Ono K. On the Arnold conjecture for weakly monotone symplectic manifolds. Invent. Math., 1995, 119(3), 519–537.
Ono K. On Arnold's conjecture for symplectic fixed points. In: Homotopy and Geometry (Warsaw, 1997). Editors: J. Oprea and A. Tralle. Warsaw: Polish Academy of Sciences, Institute of Mathematics, 1998, 13–24. (Banach Center Publ., 45.)
Pushkar' P. E. Generating functions of symplectomorphisms. Funct. Anal. Appl., 1994, 28(3), 198–201.
Pushkar' P. E. Lagrangian intersections in a symplectic space. Funct. Anal. Appl., 2000, 34(4), 288–292.
Ruan Y. B. Virtual neighborhoods and pseudo-holomorphic curves. Turkish J. Math., 1999, 23(1), 161–231.
Rudyak Yu. B. On analytical applications of stable homotopy (the Arnold conjecture, critical points). Math. Z., 1999, 230(4), 659–672.
Rudyak Yu. B. On strict category weight, gradient-like flows, and the Arnold conjecture. Internat. Math. Res. Notices, 2000, 5, 271–279.
Rudyak Yu. B., Oprea J. On the Ljusternik-Schnirelmann category of symplectic manifolds and the Arnold conjecture. Math. Z., 1999, 230(4), 673–678.
Schwarz M. A quantum cup-length estimate for symplectic fixed points. Invent. Math., 1998, 133(2), 353–397.
Siebert B. Algebraic and symplectic Gromov-Witten invariants coincide. Ann. Inst. Fourier (Grenoble), 1999, 49(6), 1743–1795.
Siebert B. Symplectic Gromov-Witten invariants. In: New Trends in Algebraic Geometry (Warwick, 1996). Editors: K. Hulek, F. Catanese, C. Peters and M. Reid. Cambridge: Cambridge University Press, 1999, 375–424. (London Math. Soc. Lecture Note Ser., 264.)
Sikorav J.-C. Points fixes d'un symplectomorphisme homologue à l'identité. C. R. Acad. Sci. Paris, Sér. I Math., 1984, 299(8), 343–346.
Sikorav J.-C. Points fixes d'une application symplectique homologue à l'identité. J. Differ. Geom., 1985, 22(1), 49–79.
Sikorav J.-C. Un problème de disjonction par isotopie symplectique dans un fibré cotangent. Ann. Sci. École Norm. Sup., Sér. 4, 1986, 19(4), 543–552.
Sikorav J.-C. Problèmes d'intersections et de points fixes en géométrie hamiltonienne. Comment. Math. Helvetici, 1987, 62(1), 62–73.
Sikorav J.-C. Quelques propriétés des plongements lagrangiens. Mém. Soc. Math. France (N. S.), 1991, 46, 151–167.
Weinstein A.C0 perturbation theorems for symplectic fixed points and Lagrangian intersections. In: Séminaire Sud-Rhodanien de Géométrie. III (Lyon, 1983). Géométrie Symplectique et de Contact: autour du Théorème de Poincaré-Birkhoff. Editors: P. Dazord and N. Desolneux-Moulis. Travaux en Cours. Paris: Hermann, 1984, 140–144.
Weinstein A. Symplectic reduction and fixed points. In: Géométrie Symplectique et Mécanique (Balaruc, 1983). Editor: J.-P. Dufour. Travaux en Cours. Paris: Hermann, 1985, 140–148.
Weinstein A. Critical point theory, symplectic geometry and Hamiltonian systems. In: Proceedings of the 1983 Beijing Symposium on Differential Geometry and Differential Equations. Editors: Shan Tao Liao and S. S. Chern. Beijing: Science Press, 1986, 261–289.
Weinstein A. On extending the Conley-Zehnder fixed point theorem to other manifolds. In: Nonlinear Functional Analysis and its Applications (University of California, 1983). Part 2. Editor: F. E. Browder. Providence, RI: Amer. Math. Soc., 1986, 541–544. (Proc. Symposia Pure Math., 45.)
Zehnder E. The Arnold conjecture for fixed points of symplectic mappings and periodic solutions of Hamiltonian systems. In: Proceedings of the International Congress of Mathematicians (Berkeley, 1986), Vol. 2. Editor: A. M. Gleason. Providence, RI: Amer. Math. Soc., 1987, 1237–1246.
1973-3 — V. M. Zakalyukin
Chiappori P. A., Ekeland I. Problèmes d'agrégation en théorie du consommateur et calcul différentiel extérieur. C. R. Acad. Sci. Paris, Sér. I Math., 1996, 323(5), 565–570.
Ekeland I. La modélisation mathématiques en économie. Gaz. Math., Soc. Math. France, 1998, 78, 51–62.
Zakalyukin V. M. Concave Darboux theorem. C. R. Acad. Sci. Paris, Sér. I Math., 1998, 327(7), 633–638.
1973-4
Arnold V. I. Algebraic unsolvability of the problem of Lyapunov stability and the problem of topological classification of singular points of an analytic system of differential equations. Funct. Anal. Appl., 1970, 4(3), 173–180.
Arnold V. I. Algebraic unsolvability of the problem of stability and the problem of topological classification of singular points of analytic systems of differential equations. Uspekhi Mat. Nauk, 1970, 25(2), 265–266 (in Russian).
Arnold V. I. Local problems of analysis. Moscow Univ. Math. Bull, 1970, 25(2), 77–80.
Arnold V. I. Problèmes résolubles et problèmes irrésolubles analytiques et géométriques. In: Passion des Formes. Dynamique Qualitative Sémiophysique et Intelligibilité. Dédié à R. Thom. Fontenay-St Cloud: ENS Éditions, 1994, 411–417; In: Formes et Dynamique, Renaissance d'un Paradigme. Hommage à René Thom. Paris: Eshel, 1995. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 577–582.]
1973-5 — A. A. Davydov
Arnold V. I. Surfaces defined by hyperbolic equations. Math. Notes, 1988, 44(1), 489–497. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 397–412.]
Arnold V. I. Catastrophe Theory. Berlin: Springer, 1992. [The Russian original 1990.]
Arnold V. I. Contact structure, relaxational oscillations and singular points of implicit differential equations. In: Global Analysis—Studies and Applications, III. Editors: Yu. G. Borisovich and Yu. E. Gliklikh. Berlin: Springer, 1988, 173–179. (Lecture Notes in Math., 1334.)
Bruce J. W., Tari F. On the multiplicity of implicit differential equations. J. Differ. Equations, 1998, 148(1), 122–147.
Bruce J. W., Fletcher G. J., Tari F. Bifurcations of implicit differential equations. Proc. Roy. Soc. Edinburgh, Sect. A, 2000, 130(3), 485–506.
Cibrario M. Sulla riduzione a forma canonica delle equazioni lineari alle derivate parziali di secondo ordine di tipo misto. Ist. Lombardo, Rend., Ser. II, 1932, 65, 889–906.
Davydov A. A. Normal form of a differential equation, not solvable for the derivative, in a neighborhood of a singular point. Funct. Anal. Appl., 1985, 19(2), 81–89.
Davydov A. A. Structural stability of control systems on orientable surfaces. Math. USSR, Sb., 1992, 72(1), 1–28.
Davydov A. A., Rosales-González E. The complete classification of typical second-order linear partial-differential equations on the plane. Dokl. Math., 1996, 54(2), 669–672.
Davydov A. A., Ortiz-Bobadilla L. Smooth normal forms of folded elementary singular points. J. Dynam. Control Systems, 1995, 1(4), 463–482.
Hayakawa A., Ishikawa G., Izumiya S., Yamaguchi K. Classification of generic integral diagrams and first order ordinary differential equations. Intern. J. Math., 1994, 5(4), 447–489.
Guzman A. Ph.D. Thesis, UNAM, Mexico, 1994.
Kossowski M. Fiber completions, contact singularities and single valued solutions for C∞-second order ODE. Canad. J. Math., 1996, 48(4), 849–870.
Kuz'min A. G. Nonclassical Equations of Mixed Type and Their Applications to Gas Dynamics. Basel: Birkhäuser, 1992. (Internat. Ser. Numer. Math., 109.)
Lemasurier M. Singularities of implicit second order differential equations. Ph. D. Thesis, University of Georgia, 1998.
Medveď M. Qualitative properties of generalized vector. Rivista Mat. Pura Appl., 1994, 15, 7–31.
Pazij N. D. Normal forms of transversally singular quasilinear Sobolev systems. Differ. Equations, 1996, 32(6), 850–852.
Pazij N. D. Ph. D. Thesis, Chelyabinsk State University, 1999 (in Russian).
Takens F. Geometric aspects of non-linear R. L. C. networks. In: Dynamical Systems—Warwick 1974. Editor: A. Manning. Berlin-Heidelberg: Springer, 1975, 305–331. (Lecture Notes in Math., 468.)
ZhitomirskiĬ M. Ya. Local normal forms for constrained systems on two manifolds. Bol. Soc. Brasil. Mat. (N. S.), 1993, 24(2), 211–232.
1973-7 — S. M. Gusein-Zade
Brieskorn E. Special singularities-resolution, deformation and monodromy. Lecture notes prepared in connection with the Summer Institute on Algebraic Geometry held at Humboldt State University in Arcata, California. Providence, RI: Amer. Math. Soc., 1974.
Luengo I. The µ-constant stratum is not smooth. Invent. Math., 1987, 90(1), 139–152.
Arnold V. I., Vassiliev V. A., Goryunov V. V., Lyashko O. V. Singularities. I. Local and Global Theory. Berlin: Springer, 1993, Ch. 2, Sect. 1.11. (Encyclopædia Math. Sci., 6; Dynamical Systems, VI.) [The Russian original 1988.]
1973-8 — S. M. Gusein-Zade
Gabrielov A. M. Bifurcations, Dynkin diagrams, and modality of isolated singularities. Funct. Anal. Appl., 1974, 8(2), 94–98.
1973-10 — V. I. Arnold
Arnold V. I. Remarks on the stationary phase method and Coxeter numbers. Russian Math. Surveys, 1973, 28(5), 19–48.
Arnold V. I. Normal forms of functions in neighborhoods of degenerate critical points. Russian Math. Surveys, 1974, 29(2), 10–50.
1973-11 — V. I. Arnold
Arnold V. I., Vassiliev V. A., Goryunov V. V., Lyashko O. V. Singularities. I. Local and Global Theory. Berlin: Springer, 1993, Ch. 1, Sect. 3.4. (Encyclopædia Math. Sci., 6; Dynamical Systems, VI.) [The Russian original 1988.]
1973-15
Arnold V. I. Critical points of functions on a manifold with a boundary, the simple Lie groups Bk, Ck, F4 and singularities of evolutes. Russian Math. Surveys, 1978, 33(5), 99–116.
Arnold V. I. Lagrange and Legendre cobordisms, I; II. Funct. Anal. Appl., 1980, 14(3), 167–177; 14(4), 252–260.
Barannikov S. A. The framed Morse complex and its invariants. In: Singularities and Bifurcations. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1994, 93–115. (Adv. Sov. Math., 21.)
1973-17 — S. M. Gusein-Zade
Gusein-Zade S. M., Nekhoroshev N. N. On adjacencies of singularities Ak to points of the μ = const stratum of a singularity. Funct. Anal. Appl., 1983, 17(4), 312–313.
1973-17 — V. A. Vassiliev
A'Campo N. Le groupe de monodromie du déploiement des singularités isolées de courbes planes, I. Math. Ann., 1975, 213(1), 1–32.
Gusein-Zade S. M. Dynkin diagrams for singularities of functions of two variables. Funct. Anal. Appl., 1974, 8(4), 295–300.
Gusein-Zade S. M., Nekhoroshev N. N. On adjacencies of singularities Ak to points of the μ = const stratum of a singularity. Funct. Anal. Appl., 1983, 17(4), 312–313.
Gusein-Zade S. M., Nekhoroshev N. N. Singularities of type Ak on plane curves of a chosen degree. Funct. Anal. Appl., 2000, 34(3), 214–215.
1973-19 — V. A. Vassiliev
A'Campo N. Le groupe de monodromie du déploiement des singularités isolées de courbes planes. II. In: Proceedings of the International Congress of Mathematicians (Vancouver, 1974), Vol. 1. Montreal: Canadian Mathematical Congress, 1975, 395–404.
1973-23 — V. I. Arnold, B. A. Khesin
Arnold V. I. The asymptotic Hopf invariant and its applications. In: Proceedings of the All-Union School on Differential Equations with Infinitely Many Independent Variables and on Dynamical Systems with Infinitely Many Degrees of Freedom (Dilizhan, May 21–June 3, 1973). Yerevan: AS of Armenian SSR, 1974, 229–256 (in Russian). [The English translation: Selecta Math. Sov., 1986, 5(4), 327–345.] [The Russian original is reprinted and supplemented in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 215–236.]
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
Gambaudo J.-M., Ghys É. Enlacements asymptotiques. Topology, 1997, 36(6), 1355–1379.
Vogel T. I. On the asymptotic linking number. Commun. Math. Phys., to appear. [Internet: http://www.arXiv.org/abs/math.DS/0011159]
1973-24 — B. A. Khesin
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
Schwarz A.S. The partition function of degenerate quadratic functional and Ray-Singer invariants. Lett. Math. Phys., 1977/78, 2(3), 247–252.
1973-25 — B. A. Khesin, A. M. Lukatskiĭ
Arnold V. I. The asymptotic Hopf invariant and its applications. In: Proceedings of the All-Union School on Differential Equations with Infinitely Many Independent Variables and on Dynamical Systems with Infinitely Many Degrees of Freedom (Dilizhan, May 21–June 3, 1973). Yerevan: AS of Armenian SSR, 1974, 229–256 (in Russian). [The English translation: Selecta Math. Sov., 1986, 5(4), 327–345.] [The Russian original is reprinted and supplemented in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 215–236.]
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
Freedman M. Zeldovich's neutron star and the prediction of magnetic froth. In: The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (Toronto, 1997). Editors: E. Bierstone, B. A. Khesin, A. G. Khovanskiĭ and J.E. Marsden. Providence, RI: Amer. Math. Soc, 1999, 165–172. (Fields Inst. Commun., 24.)
Freedman M. H., He Z.-X. Divergence-free fields: energy and asymptotic crossing number. Ann. Math., Sen 2, 1991, 134(1), 189–229.
Moffatt H. K. The degree of knottedness of tangled vortex lines. J. Fluid Mech., 1969, 35, 117–129.
1973-26 — B. A. Khesin, A. M. Lukatskiĭ
Arnold V. I. The asymptotic Hopf invariant and its applications. In: Proceedings of the All-Union School on Differential Equations with Infinitely Many Independent Variables and on Dynamical Systems with Infinitely Many Degrees of Freedom (Dilizhan, May 21–June 3, 1973). Yerevan: AS of Armenian SSR, 1974, 229–256 (in Russian). [The English translation: Selecta Math. Sov., 1986, 5(4), 327–345.] [The Russian original is reprinted and supplemented in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 215–236.]
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
Morgulisa., Yudovich V. I., Zaslavsky G. M. Compressible helical flows. Commun. Pure Appl. Math., 1995, 48(5), 571–582.
1973-27 — A. A. Glutsyuk, S. K. Lando
Arnold V. I. Critical points of functions and the classification of caustics. Uspekhi Mat. Nauk, 1974, 29(3), 243–244 (in Russian). [Reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 213–214.]
Arnold V. I. Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges. Funct. Anal. Appl., 1996, 30(1), 1–14.
Glutsyuk A. A. An analogue of Cayley's theorem for cyclic symmetric connected graphs with one cycle that are associated with generalized Lyashko-Looijenga coverings. Russian Math. Surveys, 1993, 48(2), 182–183.
Looijenga E. J. N. The complement of the bifurcation variety of a simple singularity. Invent. Math., 1974, 23(2), 105–116.
Lyashko O. V. The geometry of bifurcation diagrams. Russian Math. Surv., 1979, 34(3), 209–210.
Lyashko O. V. Geometry of bifurcation diagrams. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics, Vol. 22. Moscow: VINITI, 1983, 94–129 (in Russian). [The English translation: J. Sov. Math., 1984, 27, 2736–2759.]
Zvonkine D. A., Lando S. K. On multiplicities of the Lyashko-Looijenga mapping on discriminant strata. Funct. Anal. Appl., 2000, 33(3), 178–188.
1974-2
Givental A. B. Lagrangian imbeddings of surfaces and unfolded Whitney umbrella. Funct. Anal. Appl., 1986, 20(3), 197–203.
1974-4 — V. I. Arnold
Givental A. B. Singular Lagrangian manifolds and their Lagrangian maps. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics. Newest Results, Vol. 33. Moscow: VINITI, 55–112 (in Russian). [The English translation: J. Sov. Math., 1990, 52(4), 3246–3278.]
Shcherbak O. P. Wavefront and reflection groups. Russian Math. Surveys, 1988, 43(3), 149–194.
1974-5 — V. V. Goryunov
Baines C. E. Topics in functions with symmetry. Ph. D. Thesis, University of Liverpool, 2000.
Goryunov V. V. Unitary reflection groups associated with singularities of functions with cyclic symmetry. Russian Math. Surveys, 1999, 54(5), 873–893.
Goryunov V. V. Unitary reflection groups and automorphisms of simple hypersurface singularities. In: New developments in singularity theory (Cambridge, 2000). Editors: D. Siersma, C. T. C. Wall and V. Zakalyukin. Dordrecht: Kluwer Acad. Publ., 2001, 305–328. (NATO Sci. Ser. II Math. Phys. Chem., 21.)
Goryunov V. V., Baines C. E. Cyclically equivariant function singularities and unitary reflection groups G(2m,2,n), G9, G31. St. Petersburg Math. J., 2000, 11(5), 761–774.
Popov V. L. Discrete complex reflection groups. Commun. Math. Inst., Rijksuniv. Utrecht, 1982, 15, 89 pp.
Shephard G. C., Todd J. A. Finite unitary reflection groups. Canad. J. Math., 1954, 6, 274–304.
Słodowy P. Simple singularities and complex reflections. In: New Developments in Singularity Theory (Cambridge, 2000). Dordrecht: Kluwer Acad. Publ., 2001, 329–348. (NATO Sci. Ser. II Math. Phys. Chem., 21.)
1974-6 — V. I. Arnold, B. A. Khesin
Arnold V. I. The first steps of symplectic topology. Russian Math. Surveys, 1986, 41(6), 1–21. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 365–389.]
Arnold V. I. First steps of symplectic topology. In: VIIIth International Congress on Mathematical Physics (Marseille, 1986). Editors: M. Mebkhout and R. Sénéor. Singapore: World Scientific, 1987, 1–16.
Arnold V. I. Mysterious Mathematical Trinites. The Topological Economy Principle in Algebraic Geometry. Moscow: Moscow Center for Continuous Mathematical Education Press, 1997 (in Russian).
Arnold V. I. Symplectization, complexification and mathematical trinities. In: The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (Toronto, 1997). Editors: E. Bierstone, B. A. Khesin, A. G. Khovanskiĭ and J. E. Marsden. Providence, RI: Amer. Math. Soc., 1999, 23–37. (Fields Institute Commun., 24.); CEREMADE (UMR 7534), Université Paris-Dauphine, № 9815, 04/03/1998. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
Arnold V. I. Polymathematics: is mathematics a single science or a set of arts? In: Mathematics: Frontiers and Perspectives. Editors: V.I. Arnold, M. Atiyah, P. Lax and B. Mazur. Providence, RI: Amer. Math. Soc., 2000, 403–416; CEREMADE (UMR 7534), Université Paris-Dauphine, № 9911, 10/03/1999. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
Khesin B. A. Informal complexification and Poisson structures on moduli spaces. In: Topics in Singularity Theory. V.I. Arnold's 60th Anniversary Collection. Editors: A. Khovanskiĭ, A. Varchenko and V. Vassiliev. Providence, RI: Amer. Math. Soc, 1997, 147–155. (AMS Transl., Ser. 2, 180; Adv. Math. Sci., 34.)
Khesin B. A., Rosly A. A. Polar homology and holomorphic bundles. Phil. Trans. Roy. Soc. London, Ser. A, 2001, 359, 1413–1427.
Khesin B. A., Rosly A. A. Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces. In: The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (Toronto, 1997). Editors: E. Bierstone, B. A. Khesin, A. G. Khovanskiĭ and J. E. Marsden. Providence, RI: Amer. Math. Soc, 1999, 311–323. (Fields Inst. Commun., 24.)
1974-7 — S. V. Chmutov
Arnold V. I. Critical points of functions on a manifold with boundary, the simple Lie groups Bk, Ck, F4, and singularities of evolutes. Russian Math. Surveys, 1978, 33(5), 99–116.
Arnold V. I., Vassiliev V. A., Goryunov V. V., Lyashko O. V. Singularity Theory. II. Classification and Applications. Berlin: Springer, 1993. (Encyclopædia Math. Sci., 39; Dynamical Systems, VIII.) [The Russian original 1989.]
Chmutov S. V., Varchenko A. N. Finite irreducible groups, generated by reflections, are monodromy groups of appropriate singularities. Funct. Anal. Appl., 1984, 18(3), 171–183.
Lyashko O. V. Classification of critical points of functions on a manifold with singular boundary. Funct. Anal. Appl., 1983, 17(3), 187–193.
Roberts R. M., Zakalyukin V. M. Symmetric wavefronts, caustic and Coxeter groups. In: Singularity Theory (Trieste, 1991). Editors: D. T. Lê, K. Saito and B. Teissier. River Edge, NJ: World Scientific, 1995, 594–626.
Shcherbak I. G. Duality of boundary singularities. Russian Math. Surveys, 1984, 39(2), 195–196.
Shcherbak I. G. Singularities in the presence of symmetries. In: Topics in Singularity Theory. V. I. Arnold's 60th Anniversary Collection. Editors: A. Khovanskiĭ, A. Varchenko and V. Vassiliev. Providence, RI: Amer. Math. Soc., 1997, 189–196. (AMS Transl., Ser. 2, 180; Adv. Math. Sci., 34.)
Wall C. T. C. A note on symmetry of singularities. Bull. London Math. Soc., 1980, 12(3), 169–175.
Wall C. T. C. A second note on symmetry of singularities. Bull. London Math. Soc., 1980, 12(5), 347–354.
Wasserman G. Classification of singularities with compact abelian symmetry. Regensburg Math. Schrift, 1977, 1, 284 pp.
1974-8 — I. A. Bogaevsky
Arnold V. I. Wave front evolution and equivariant Morse lemma. Commun. Pure Appl. Math., 1976, 29(6), 557–582; correction: 1977, 30(6), 823. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 289–318.]
Arnold V. I. Singularities of Caustics and Wave Fronts. Dordrecht: Kluwer Acad. Publ., 1990. (Math. Appl., Sov. Ser., 62.)
Arnold V. I. Catastrophe Theory. Berlin: Springer, 1992. [The Russian original 1990.]
Arnold V. I., Gusein-Zade S. M., Varchenko A. N. Singularities of Differentiable Maps, Vol. I: The classification of critical points, caustics and wave fronts. Boston, MA: Birkhäuser, 1985. (Monographs in Math., 82.) [The Russian original 1982.]
Bogaevsky I. A. Perestroikas of fronts in evolutionary families. Proc. Steklov Inst. Math., 1995, 209, 57–72.
Zakalyukin V. M. Reconstructions of wave fronts depending on one parameter. Funct. Anal. Appl., 1976, 10(2), 139–140.
Zakalyukin V. M. Reconstructions of fronts and caustics depending on a parameter and versality of mappings. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics, Vol. 22. Moscow: VINITI, 1983, 56–93 (in Russian). [The English translation: J. Sov. Math., 1984, 27, 2713–2735.]
1975-6 — A. M. Gabrielov
Gabrielov A. M., Kushnirenko A. G. Description of deformations with constant Milnor number for homogeneous functions. Funct. Anal. Appl., 1975, 9(4), 329–331.
1975-7 — V. A. Vassiliev
Vassiliev V. A., Serganova V. V. On the number of real and complex moduli of singularities of smooth functions and matroid realizations. Math. Notes, 1991, 49(1), 15–20.
1975-9 — V. I. Arnold
Arnold V. I. Critical points of smooth functions and their normal forms. Russian Math. Surveys, 1975, 30(5), 1–75.
Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997.
1975-12 — S. M. Gusein-Zade
Gusein-Zade S. M. Dynkin diagrams for singularities of functions of two variables. Funct. Anal. Appl., 1974, 8(4), 295–300.
A'Campo N. Le groupe de monodromie du deploiement des singularités isolées de courbes planes, I. Math. Ann., 1975, 213(1), 1–32.
1975-13 — S. V. Chmutov
Chmutov S. V. Spectrum and equivariant deformations of critical points. Uspekhi Mat. Nauk, 1984, 39(4), 113–114 (in Russian).
Chmutov S. V. Extremal distributions of critical points and critical values. In: Singularity Theory (Trieste, 1991). Editors: D. T. Lê, K. Saito and B. Teissier. River Edge, NJ: World Scientific, 1995, 192–205.
1975-15 — S. M. Gusein-Zade
Gusein-Zade S. M. On singularities from which an A1 can be split off. Funct. Anal. Appl., 1993, 27(1), 57–60.
1975-17 — V. V. Goryunov
Arnold V. I., Vassiliev V. A., Goryunov V. V., Lyashko O. V. Singularities. II. Classification and Applications. Berlin: Springer, 1993, Ch. 1, Sect. 4. (Encyclopædia Math. Sci., 39; Dynamical Systems, VIII.) [The Russian original 1989.]
Pellikaan R. On hypersurface singularities which are stems. Compos. Math., 1989, 71(2), 229–240.
Pellikaan R. Series of isolated singularities. In: Singularities (Iowa City, IA, 1986). Editor: R. Randell. Providence, RI: Amer. Math. Soc., 1989, 241–259. (Contemp. Math., 90.)
Siersma D. Isolated line singularities. In: Singularities. Part 2 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 485–496. (Proc. Symposia Pure Math., 40.)
Siersma D. Singularities with critical locus a 1-dimensional complete intersection and transversal type A1, Topology Appl., 1987, 27(1), 51–73.
Siersma D. Variation mappings on singularities with a 1-dimensional critical locus. Topology, 1991, 30(3), 445–469.
Siersma D. The vanishing topology of non isolated singularities. In: New Developments in Singularity Theory (Cambridge, 2000). Editors: D. Siersma, C. T. C. Wall and V. Zakalyukin. Dordrecht: Kluwer Acad. Publ., 2001, 447–472. (NATO Sci. Ser. II Math. Phys. Chem., 21.)
1975-17 — S. M. Gusein-Zade
Siersma D. Periodicities in Arnold's lists of singularities. In: Real and Complex Singularities (Oslo, 1976). Editor: P. Holm. Alphen aan den Rijn: Sijthoff & Noordhoff, 1977, 497–524.
1975-18 — V. A. Vassiliev
Lyashko O. V. Decompositions of simple singularities of functions. Funct. Anal. Appl., 1976, 10(2), 122–128.
1975-19 — V. A. Vassiliev
Nekrasov N. A. On the cohomology of the complement of the bifurcation diagram of the singularity Aμ. Funct. Anal. Appl., 1993, 27(4), 245–250.
Vassiliev V. A. Stable cohomologies of the complements of the discriminants of deformations of singularities of smooth functions. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics. Newest Results, Vol. 33. Moscow: VINITI, 1988, 3–29 (in Russian). [The English translation: J. Sov. Math., 1990, 52(4), 3217–3230.]
Vassiliev V. A. Complements of Discriminants of Smooth Maps: Topology and Applications, revised edition. Providence, RI: Amer. Math. Soc., 1994. (Transl. Math. Monographs, 98.)
1975-20 — V. I. Arnold
Arnold V. I. First steps of local symplectic algebra. CEREMADE (UMR 7534), Université Paris-Dauphine, № 9902, 20/01/1999; In: Differential Topology, Infinite-Dimensional Lie Algebras, and Applications. D. B. Fuchs’ 60th Anniversary Collection. Editors: A. Astashkevich and S. Tabachnikov. Providence, RI: Amer. Math. Soc., 1999, 1–8. (AMS Transl., Ser. 2, 194; Adv. Math. Sci., 44.) [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
Arnold V. I. First steps of local contact algebra. CEREMADE (UMR 7534), Université Paris-Dauphine, № 9909, 10/02/99; Canad. J. Math., 1999, 51(6), 1123–1134.
Arnold V. I. Simple singularities of curves. CEREMADE (UMR 7534), Université Paris-Dauphine, № 9906, 09/02/1999; Proc. Steklov Inst. Math., 1999, 226, 20–28. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
Bruce J. W., Gaffney T. J. Simple singularities of mappings (ℂ,0) → (ℂ2,0). J. London Math. Soc., Ser. 2, 1982, 26(3), 465–474.
1975-20 — V. V. Goryunov
Gibson C. G., Hobbs C. A. Simple singularities of space curves. Math. Proc. Cambridge Phil. Soc., 1993, 113(2), 297–310.
Goryunov V. V. Singularities of projections of complete intersections. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics, Vol. 22. Moscow: VINITI, 1983, 167–206 (in Russian). [The English translation: J. Sov. Math., 1984, 27, 2785–2811.]
Goryunov V. V. Projections of generic surfaces with boundaries. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 157–200. (Adv. Sov. Math., 1.)
Houston K. On the classification and topology of complex multi-germs of corank one and codimension one. Preprint, University of Leeds, December 2001.
Houston K. On the classification of real mono-germs of corank one and codimension one. Preprint, University of Leeds, February 2002.
Houston K., Kirk N. On the classification and geometry of corank 1 map-germs from three-space to four-space. In: Singularity Theory (Liverpool, 1996). Editors: B. Bruce and D. Mond. Cambridge: Cambridge University Press, 1999, 325–351. (London Math. Soc. Lecture Note Ser., 263.)
Mond D. On the classification of germs of maps from \(\mathbb{R}^2 \) to \(\mathbb{R}^3 \). Proc. London Math. Soc., Ser. 3, 1985, 50(2), 333–369.
Mond D. Singularities of mappings from surfaces to 3-space. In: Singularity theory (Trieste, 1991). Editors: D. T. Lê, K. Saito and B. Teissier. River Edge, NJ: World Scientific, 1995, 509–526.
Wik Atique R. On the classification of multi-germs of maps from ℂ2 to ℂ3 under \(A\)-equivalence. In: Real and Complex Singularities (Saõ Carlos, 1998). Editors: J. W. Bruce and F. Tari. Boca Raton, FL: Chapman and Hall, 2000, 119–133. (Chapman and Hall/CRC Res. Notes in Math., 412.)
1975-21
Arnold V. I., Varchenko A. N., Givental A. B., KhovanskiĬ A. G. Singularities of functions, wave fronts, caustics and multidimensional integrals. In: Mathematical Physics Reviews, Vol. 4. Editor: S. P. Novikov. Chur: Harwood Acad. Publ., 1984, 1–92. (Sov. Sci. Rev., Sect. C: Math. Phys. Rev., 4.)
1975-22
Arnold V. I., Gusein-Zade S. M., Varchenko A. N. Singularities of Differentiable Maps, Vol. II: Monodromy and Asymptotics of Integrals. Boston, MA: Birkhäuser, 1988. (Monographs in Math., 83.) [The Russian original 1984.]
1975-23 — V. I. Arnold
Arnold V. I. On some problems in singularity theory. In: Geometry and Analysis. Papers dedicated to the memory of V. K. Patodi. Bangalore: Indian Acad. Sci., 1980, 1–9. [Reprinted in: Proc. Indian Acad. Sci. Math. Sci., 1981, 90(1), 1–9.]
Arnold V. I., OleĬnik O. A. Topology of real algebraic varieties. Moscow Univ. Math. Bull., 1979, 34(6), 5–17.
1975-24 — V. A. Vassiliev
Vassiliev V. A. Stable cohomologies of the complements of the discriminants of deformations of singularities of smooth functions. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics. Newest Results, Vol. 33. Moscow: VINITI, 1988, 3–29 (in Russian). [The English translation: J. Sov. Math., 1990, 52(4), 3217–3230.]
Vassiliev V. A. Topology of complements to discriminants and loop spaces. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 9–21. (Adv. Sov. Math., 1.)
Vassiliev V. A. Complements of Discriminants of Smooth Functions: Topology and Applications, revised edition. Providence, RI: Amer. Math. Soc., 1994. (Transl. Math. Monographs, 98.)
1975-25 — V. I. Arnold
Arnold V. I. Wave front evolution and equivariant Morse lemma. Commun. Pure Appl. Math., 1976, 29(6), 557–582; correction: 1977, 30(6), 823. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow, PHASIS, 1997, 289–318.]
Arnold V. I. Lagrange and Legendre cobordisms, I; II. Funct. Anal. Appl., 1980, 14(3), 167–177; 14(4), 252–260.
Arnold V. I. On some nonlinear problems. In: Crafoord Prize in Mathematics, 1982. Crafoord Lectures. Stockholm: The Royal Swedish Academy of Sciences, 1982, 1–7. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 335–344.]
Arnold V. I. On the Newton attraction of gatherings of dust-like particles. Uspekhi Mat. Nauk, 1982, 37(4), 125 (in Russian).
Arnold V. I. On the Newton potential of hyperbolic layers. Trudy Tbilis. Univ., Ser. Mat., Mekh., Astron., 1982, 232/233(13–14), 23–29 (in Russian). [The English translation: Selecta Math. Sov., 1985, 4(2), 103–106.]
Arnold V. I. Reconstructions of singularities of potential flows in a collision-free medium and caustic metamorphoses in three-dimensional space. Trudy Semin. Petrovskogo, 1982, 8, 21–57 (in Russian). [The English translation: J. Sov. Math., 1986, 32(3), 229–257.]
Arnold V. I. Some algebro-geometrical aspects of the Newton attraction theory. In: Arithmetic and Geometry. Papers dedicated to I. R. Shafarevich, Vol. II: Geometry. Basel: Birkhäuser, 1983, 1–3. (Progr. Math., 36.)
Arnold V. I. Singularities of Caustics and Wave Fronts. Dordrecht: Kluwer Acad. Publ., 1990. (Math. Appl., Sov. Ser., 62.)
Arnold V. I. Mathematical problems in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math. Sci., 100.) [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.]
Arnold V. I., Baryshnikov Yu. M., BogaevskiĬ I. A. Supplement 2 in: Gurbatov S. N., Malakhov A. N., Saichev A. I. Nonlinear Random Waves and Turbulence in Nondispersive Media: Waves, Rays, Particles. Translated from Russian. Manchester: Manchester University Press, 1991. (Nonlinear Science: Theory and Applications.)
Arnold V. I., Zeldovich Ya. B., Shandarin S. F. Elements of the large scale structure of the Universe. Uspekhi Mat. Nauk, 1981, 36(3), 244–245 (in Russian).
Arnold V. I., Zeldovich Ya. B., Shandarin S. F. The large scale structure of the Universe. I. General properties. One-and two-dimensional models. Geophys. Astrophys. Fluid Dynamics, 1982, 20(1–2), 111–130.]
Bakhtin V. I. Topologically normal forms of caustic transformations of Dμ-series. Moscow Univ. Math. Bull., 1987, 42(4), 63–66.
Roytvarf A. A. The motion of a continuous medium in the force field with a rooted singularity. Moscow Univ. Mech. Bull., 1987, 42(1), 24–27.
Roytvarf A. A. On the dynamics of a one-dimensional self-gravitating medium. Physica D, 1994, 73(3), 189–204.
Stanchenko S. V. Arbitrary deformations of Lagrangian and Legendrian mappings Proc. Steklov Inst. Math., 1995, 209, 191–202.
1975-26 — V. I. Arnold
Arnold V. I. Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect. Selecta Math. (N. S.), 1995, 1(1), 1–19. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 583–604.]
Arnold V. I. Relatives of the quotient of the complex projective plane by complex conjugation. Proc. Steklov Inst. Math., 1999, 224, 46–56. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
Arnold V. I. Symplectization, complexification and mathematical trinities. In: The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (Toronto, 1997). Editors: E. Bierstone, B. A. Khesin, A. G. Khovanskiĭ and J. E. Marsden. Providence, RI: Amer. Math. Soc., 1999, 23–37. (Fields Institute Commun., 24.); CEREMADE (UMR 7534), Université Paris-Dauphine, № 9815, 04/03/1998. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
Arnold V. I., Kozlov V. V., NeĬshtadt A. I. Mathematical Aspects of Classical and Celestial Mechanics, 2nd edition. Berlin: Springer, 1993. (Encyclopædia Math. Sci., 3; Dynamical Systems, III.) [The Russian original 1985.] [The second, revised and supplemented, Russian edition 2002.]
MaĬlybaev A. A. On cones tangent to the stability domain of a family of real matrices. Vestnik Moskov. Univ. Ser. Mat. Mekh., 1998, № 6, 51–54 (in Russian, for the English translation see Moscow Univ. Math. Bull.).
MaĬlybaev A. A. A method for reducing families of matrices to normal forms. Dokl. Math., 1999, 60(1), 39–43.
MaĬlybaev A. A. Reducing families of matrices to their normal forms and an application to the stability theory. Fundam. Prikl. Mat., 1999, 5(4), 1111–1133 (in Russian).
MaĬlybaev A. A. Singularities of the boundaries of stability domains: analysis and applications. Ph. D. Thesis, Moscow State University, 1999 (in Russian).
MaĬlybaev A. A., SeĬranyan A. P. On singularities of the boundary of the domain of stability. Dokl. Phys., 1998, 43(4), 248–252.
MaĬlybaev A. A., SeĬranyan A. P. Singularities of the boundaries of stability domains. J. Appl. Math. Mech., 1998, 62(6), 909–920.
MaĬlybaev A. A., SeĬranyan A. P. The stability domains of Hamiltonian systems. J. Appl. Math. Mech., 1999, 63(4), 545–555.
Postnikov A. E., Shapiro B. Z., Shapiro M. Z. Algebras of curvature forms on homogeneous manifolds. In: Differential Topology, Infinite-Dimensional Lie Algebras, and Applications. D. B. Fuchs’ 60th Anniversary Collection. Editors: A. Astashkevich and S. Tabachnikov. Providence, RI: Amer. Math. Soc., 1999, 227–235. (AMS Transl., Ser. 2, 194; Adv. Math. Sci., 44.)
SeĬranyan A. P., MaĬlybaev A. A. On singularities of the stability domain boundaries of Hamiltonian and gyroscopic systems. Dokl. Phys., 1999, 44(4), 251–255.
Shapiro M. Z., Vainshtein A. D. Stratification of Hermitian matrices and the Alexander mapping. C. R. Acad. Sci. Paris, Sér. I Math., 1995, 321(12), 1599–1604.
Shapiro B. Z., Shapiro M. Z. On ring generated by Chern 2-forms on SLn/\(B\). C. R. Acad. Sci. Paris, Sér. I Math., 1998, 326(1), 75–80.
1975-27 — V. I. Arnold
Arnold V. I., Varchenko A. N., Givental A. B., KhovanskiĬ A. G. Singularities of functions, wave fronts, caustics and multidimensional integrals. In: Mathematical Physics Reviews, V. 4. Editor: S. P. Novikov. Chur: Harwood Acad. Publ., 1984, 1–92. (Sov. Sci. Rev., Sect. C: Math. Phys. Rev., 4.)
Arnold V. I. Singularities of Caustics and Wave Fronts. Dordrecht: Kluwer Acad. Publ., 1990. (Math. Appl., Sov. Ser., 62.)
Arnold V. I. Mathematical problems in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math. Sci., 100.) [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.]
Karpushkin V. N. A theorem concerning uniform estimates of oscillatory integrals when the phase is a function of two variables. Trudy Semin. Petrovskogo, 1984, 10, 150–169 (in Russian). [The English translation: J. Sov. Math., 1986, 35, 2809–2826.]
Varchenko A. N. Newton polyhedra and estimation of oscillating integrals. Funct. Anal. Appl., 1976, 10(3), 175–196.
Vassiliev V. A. Asymptotic behavior of exponential integrals in the complex domain. Funct. Anal. Appl., 1979, 13(4), 239–247.
1975-28 — V. I. Arnold
Arnold V. I. On the theory of envelopes. Uspekhi Mat. Nauk, 1976, 31(3), 248–249 (in Russian).
Arnold V. I. Wave front evolution and equivariant Morse lemma. Commun. Pure Appl. Math., 1976, 29(6), 557–582; correction: 1977, 30(6), 823. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 289–318.]
Arnold V. I. Lagrangian manifolds with singularities, asymptotic rays and the unfurled swallowtail. Funct. Anal. Appl., 1981, 15(4), 235–246.
Arnold V. I. Sweeping a caustic by the return edge of a moving front. Uspekhi Mat. Nauk, 1981, 36(4), 233 (in Russian).
Arnold V. I. Asymptotic rays in the symplectic geometry. Uspekhi Mat. Nauk, 1982, 37(2), 182–183.
Arnold V. I. Singularities in variational calculus. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics, Vol. 22. Moscow: VINITI, 1983, 3–55 (in Russian). [The English translation: J. Sov. Math., 1984, 27, 2679–2713.]
Arnold V. I. Singularities of systems of rays. Russian Math. Surveys, 1983, 38(2), 87–176.
Arnold V. I. Singularities of ray systems. In: Proceedings of the International Congress of Mathematicians (Warsaw, August 16–24, 1983), V. 1. Editors: Z. Ciesielski and C. Olech. Warsaw: PWN and Amsterdam: North-Holland, 1984, 27–49.
Arnold V. I. Implicit differential equations, contact structures, and relaxation oscillations. Uspekhi Mat. Nauk, 1985, 40(5), 188 (in Russian).
Arnold V. I. Contact structure, relaxation oscillations and singular points of implicit differential equations. In: Geometry and the Theory of Singularities in Nonlinear Equations. Voronezh: Voronezh University Press, 1987, 3–8 (in Russian). (Novoe v Global'nom Analize, 7.) [Reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 391–396.]
Arnold V. I., Vassiliev V. A., Goryunov V. V., Lyashko O.V. Singularities. II. Classification and Applications. Berlin: Springer, 1993. (Encyclop№dia Math. Sci., 39; Dynamical Systems, VIII.) [The Russian original 1989.]
Petris J. E. H. Normalformen für Singularitäten von einparametrigen Flächenscharen. Dissertation, ETH № 9016, Eidgenössische Technische Hochschule Zürich, 1990, 170 S.
1975-29 — A. A. Agrachev, V. I. Arnold, A. A. Davydov
Agrachev A. A. Methods of control theory in nonholonomic geometry. In: Proceedings of the International Congress of Mathematicians (Zürich, 1994). Editor: S. D. Chatterji. Basel: Birkhäuser, 1995, 1473–1483.
Agrachev A. A. Exponential mappings for contact sub-Riemannian structures. J. Dynam. Control Systems, 1996, 2(3), 321–358.
Agrachev A. A. Compactness for sub-Riemannian length-minimizers and subanalyticity. Rend. Semin. Mat. Torino, 1998, 56(4), 1–12.
Agrachev A. A., Bonnard B., Chyba M., Kupka I. Sub-Riemannian sphere in Martinet flat case. J. ESAIM: Control, Optimisation and Calculus of Variations, 1997, 2, 377–448.
Agrachev A. A., Charlot G., Gauthier J.-P. A., Zakalyukin V. M. On sub-Riemannian caustics and wave fronts for contact distributions in the three-space. J. Dynam. Control Systems, 2000, 6(3), 365–395.
Agrachev A. A., El-Alaoui C., Gauthier J.-P. A. Sub-Riemannian metrics on \(\mathbb{R}^3 \). In: Geometric Control and Non-Holonomic Mechanics (Mexico City, 1996). Editors: V. Jurdjevic and R. W. Sharpe. Providence, RI: Amer. Math. Soc., 1998, 29–78. (Canad. Math. Soc. Conf. Proc., 25.)
Agrachev A. A., Gauthier J.-P. A. On the Dido problem and plane isoperimetric problems. Acta Appl. Math., 1999, 57(3), 287–338.
Agrachev A. A., Gauthier J.-P. A. On subanalyticity of Carnot-Carathéodory distances. Ann. Institut Henri Poincaré, Analyse non linéaire, 2001, 18, 359–382.
Arnold V. I. Some open problems of the singularity theory. In: The Theory of Cubature Formulae and Applications of the Functional Analysis to Problems in Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Semin. S. L. Soboleva, 1.)
Arnold V. I. Lagrange and Legendre cobordisms, I; II. Funct. Anal. Appl., 1980, 14(3), 167–177; 14(4), 252–260.
Arnold V. I. On some problems in singularity theory. In: Geometry and Analysis. Papers dedicated to the memory of V. K. Patodi. Bangalore: Indian Acad. Sci., 1980, 1–9. [Reprinted in: Proc. Indian Acad. Sci. Math. Sci., 1981, 90(1), 1-9.]
Arnold V. I. Lagrangian manifolds with singularities, asymptotic rays and the unfurled swallowtail. Funct. Anal. Appl., 1981, 15(4), 235–246.
Arnold V. I. Sweeping a caustic by the return edge of a moving front. Uspekhi Mat. Nauk, 1981, 36(4), 233 (in Russian).
Arnold V. I. Reconstructions of singularities of potential flows in a collision-free medium and caustic metamorphoses in three-dimensional space. Trudy Semin. Petrovskogo, 1982, 8, 21–57 (in Russian). [The English translation: J. Sov. Math., 1986, 32(3), 229–257.]
Arnold V. I. Singularities of Legendre varieties, of evolvents and of fronts at an obstacle. Ergod. Theory Dynam. Systems, 1982, 2(3–4), 301–309.
Arnold V. I. Singularities in variational calculus. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics, Vol. 22. Moscow: VINITI, 1983, 3–55 (in Russian). [The English translation: J. Sov. Math., 1984, 27, 2679–2713.]
Arnold V. I. Singularities of systems of rays. Russian Math. Surveys, 1983, 38(2), 87–176.
Arnold V. I. Singularities in the calculus of variations. Uspekhi Mat. Nauk, 1984, 39(5), 256 (in Russian).
Arnold V. I. Singularities of ray systems. In: Proceedings of the International Congress of Mathematicians (Warsaw, 1983), Vol. 1. Editors: Z. Ciesielski and C. Olech. Warsaw: PWN and Amsterdam: North-Holland, 1984, 27–49.
Arnold V. I. Preface in: Griffiths P. Exterior Differential Systems and the Calculus of Variations. Translated from the English original 1983. Moscow: Mir, 1986, 5–6 (in Russian).
Arnold V. I. On the interior scattering of waves, defined by hyperbolic variational principles. J. Geom. Phys., 1988, 5(3), 305–315.
Arnold V. I. Surfaces defined by hyperbolic equations. Math. Notes, 1988, 44(1), 489–497. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 397–412.]
Arnold V. I. Singularities of Caustics and Wave Fronts. Dordrecht: Kluwer Acad. Publ., 1990. (Math. Appl., Sov. Ser., 62.)
Arnold V. I., Baryshnikov Yu. M., BogaevskiĬ I. A. Supplement 2 in: Gurbatov S. N., Malakhov A. N., Saichev A. I. Nonlinear Random Waves and Turbulence in Nondispersive Media: Waves, Rays, Particles. Translated from Russian. Manchester: Manchester University Press, 1991. (Nonlinear Science: Theory and Applications.)
Arnold V. I. Sur les propriétés topologiques des projections lagrangiennes en géométrie symplectique des caustiques. CEREMADE (UMR 7534), Université Paris-Dauphine, № 9320, 14/06/1993; Rev. Mat. Univ. Complut. Madrid, 1995, 8(1), 109–119. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 525–532.]
Arnold V. I. Topological Invariants of Plane Curves and Caustics. Dean Jacqueline B. Lewis Memorial Lectures, Rutgers University. Providence, RI: Amer. Math. Soc., 1994. (University Lecture Series, 5.)
Arnold V. I. Invariants and perestroikas of plane fronts. Proc. Steklov Inst. Math., 1995, 209, 11–56.
Arnold V. I. Topological properties of Legendre projections in contact geometry of wave fronts. St. Petersburg Math. J., 1995, 6(3), 439–452.
Arnold V. I. Topological problems of the theory of wave propagation. Russian Math. Surveys, 1996, 51(1), 1–47.
Bonnard B., Launay G., Trélat E. The transcendence required for computing the sphere and wave front in the Martinet sub-Riemannian geometry. In: Proceedings of the International Conference Dedicated to the 90th Birthday of L. S. Pontryagin (Moscow, 1998), Vol. 3: Geometic Control Theory. Itogi Nauki i Tekhniki VINITI. Contemporary Mathematics and its Applications. Thematic Surveys, Vol. 64. Moscow: VINITI, 1999, 82–117 (in Russian).
Bressan A., Piccoli B. A generic classification of time-optimal planar stabilizing feedbacks. SIAM J. Control Optimization, 1998, 36(1), 12–32.
Charlot G. Quasi-contact S-R metrics: normal form in \(\mathbb{R}^{2n} \), wave front and caustic in \(\mathbb{R}^4 \). Acta Appl. Math. (to appear).
Davydov A. A., Jongen H. T. Normal forms in one-parametric optimization. Ann. Operations Research, 2001, 101, 255–265.
Davydov A. A., Zakalyukin V. M. Point singularities of the conditional minimum on a three-dimensional manifold. Proc. Steklov Inst. Math., 1998, 220, 109–125.
Davydov A. A., Zakalyukin V. M. Classification of relative minima singularities. In: Geometry and Topology of Caustics—CAUSTICS'98 (Warsaw). Editors: S. Janeczko and V. M. Zakalyukin. Warsaw: Polish Academy of Sciences, Institute of Mathematics, 1999, 75–90. (Banach Center Publ., 50.)
Davydov A. A., Zakalyukin V. M. The coincidence of generic singularities of solutions of extremal problems with constraints. In: Proceedings of the International Conference Dedicated to the 90th Birthday of L. S. Pontryagin (Moscow, 1998), Vol. 3: Geometic Control Theory. Itogi Nauki i Tekhniki VINITI. Contemporary Mathematics and its Applications. Thematic Surveys, Vol. 64. Moscow: VINITI, 1999, 118–143 (in Russian).
El-Alaoui C., Gauthier J.-P., Kupka I. Small sub-Riemannian balls on R3. J. Dynam. Control Systems, 1996, 2(3), 359–421.
Ge Zh. Horizontal path space and Carnot-Carathéodory metric. Pacific J. Math., 1993, 161(2), 255–286.
Jacquet S. Subanalyticity of the sub-Riemannian distance. J. Dynam. Control Systems, 1999, 5(3), 303–328.
Jacquet S. Regularity of the sub-Riemannian distance and cut locus. In: Nonlinear Control in the Year 2000 (Paris, 2000). Editors: A. Isidori, F. Lamnabhi-Lagarrigue and W. Respondek. London: Springer, 2000, 321–332. (Lecture Notes in Control and Inform. Sci., 258.)
Piccoli B. Classification of generic singularities for the planar time-optimal synthesis. SIAM J. Control Optimization, 1996, 34(6), 1914–1946.
Piccoli B. Regular time-optimal syntheses for smooth planar systems. Rend. Semin. Mat. Univ. Padova, 1996, 95, 59–79.
Siersma D. Properties of conflict sets in the plane. In: Geometry and Topology of Caustics—CAUSTICS'98 (Warsaw). Editors: S. Janeczko and V. M. Zakalyukin. Warsaw: Polish Academy of Sciences, Institute of Mathematics, 1999, 267–276. (Banach Center Publ., 50.)
Siersma D. Voronoĭ diagrams and Morse theory of the distance function. In: Geometry in Present Day Science (Aarhus, 1997). Editors: O. E. Barndorff-Nielsen and E. B. Vedel Jensen. Singapore: World Scientific, 1999, 187–208.
Sotomayor J., Siersma D., García R. Curvatures of conflict surfaces in Euclidean 3-space. In: Geometry and Topology of Caustics—CAUSTICS'98 (Warsaw). Editors: S. Janeczko and V. M. Zakalyukin. Warsaw: Polish Academy of Sciences, Institute of Mathematics, 1999, 277–285. (Banach Center Publ., 50.)
Sussmann H. J. Optimal control and piecewise analyticity of the distance function. In: Optimization and Nonlinear Analysis (Haifa, 1990). Editors: A. Ioffe, M. Marcus and S. Reich. Harlow: Longman and New York: John Wiley, 1992, 298–310. (Pitman Res. Notes Math. Ser., 244.)
Vershik A. M., Gershkovich V. Ya. Nonholonomic dynamical systems. Geometry of disributions and variational problems. In: Itogi nauki i Tekhniki VINITI. Current Problems in Mathematics, Vol. 16. Moscow: VINITI, 1987, 5–85 (in Russian). [The English translation in: Integrable Systems. Nonholonomic Dynamical Systems. Editors: V. I. Arnold and S. P. Novikov. Berlin: Springer, 1994, 1–81. (Encyclopædia Math. Sci., 16; Dynamical Systems, VII.)]
Zakalyukin V. M. Reconstructions of fronts and caustics depending on a parameter and versality of mappings. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics, Vol. 22. Moscow: VINITI, 1983, 56–93 (in Russian). [The English translation: J. Sov. Math., 1984, 27, 2713–2735.]
Zakalyukin V. M. Envelopes of families of wave fronts and control theory. Proc. Steklov Inst. Math., 1995, 209, 114–123.
1975-30 — V. I. Arnold
Arnold V. I. Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd edition. New York: Springer, 1988. (Grundlehren der Mathematischen Wissenschaften, 250.) [The Russian original 1978.]
Arnold V. I. Implicit differential equations, contact structures, and relaxation oscillations. Uspekhi Mat. Nauk, 1985, 40(5), 188 (in Russian).
Arnold V. I. Catastrophe theory. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics, Vol. 5. Moscow: VINITI, 1986, 219–277 (in Russian). [The English translation in: Bifurcation Theory and Catastrophe Theory. Editor: V. I. Arnold. Berlin: Springer, 1994, 207–264. (Encyclopædia Math. Sci., 5; Dynamical Systems, V.)]
Arnold V. I. Contact structure, relaxation oscillations and singular points of implicit differential equations. In: Geometry and the Theory of Singularities in Nonlinear Equations. Voronezh: Voronezh University Press, 1987, 3–8 (in Russian). (Novoe v Global'nom Analize, 7.) [Reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 391–396.]
Arnold V. I. Bifurcations and singularities in mathematics and mechanics. In: Theoretical and Applied Mechanics (XVII IUTAM Congress, Grenoble, August 21–27, 1988). Editors: P. Germain, M. Piau and D. Caillerie. Amsterdam: North-Holland, 1989, 1–25.
Arnold V. I. Contact geometry: the geometrical method of Gibbs's thermodynamics. In: Proceedings of the Gibbs Symposium (Yale University, 1989). Editors: D. G. Caldi and G. D. Mostow. Providence, RI: Amer. Math. Soc. and New York: American Institute of Physics, 1990, 163–179.
Arnold V. I. Lectures on Partial Differential Equations, 2nd supplemented edition. Moscow: PHASIS, 1997 (in Russian).
Arnold V. I., AfraĬmovich V. S., Il'yashenko Yu. S., Shil'nikov L. P. Bifurcation theory. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics, Vol. 5. Moscow: VINITI, 1986, 5–218. [The English translation in: Bifurcation Theory and Catastrophe Theory. Editor: V. I. Arnold. Berlin: Springer, 1994, 1–205. (Encyclopædia Math. Sci., 5; Dynamical Systems, V.)]
Arnold V. I., Vassiliev V. A., Goryunov V. V., Lyashko O. V. Singularities. II. Classification and Applications. Berlin: Springer, 1993, Ch. 1. (Encyclopædia Math. Sci., 39; Dynamical Systems, VIII.) [The Russian original 1989.]
Dara L. Singularités génériques des équations différentielles multiformes. Bol. Soc. Brasil. Mat., 1975, 6(2), 95–128.
Davydov A. A. Normal form of a differential equation, not solvable for the derivative, in a neighborhood of a singular point. Funct. Anal. Appl., 1985, 19(2), 81–89.
Thom R. Sur les équations différentielles multiformes et leurs intégrales singulières. Bol. Soc. Brasil. Mat., 1972, 3(1), 1–11.
1976-4 — S. L. Tabachnikov
Arnold V. I. Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd edition. New York: Springer, 1988, Sect. 1.6. (Grundlehren der Mathematischen Wissenschaften, 250.) [The Russian original 1978.]
Tabachnikov S. L. Geometry of Lagrangian and Legendrian 2-web. Differ. Geom. Appl., 1993, 3(3), 265–284.
1976-5 — B. A. Khesin
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
Khesin B. A. Ergodic interpretation of integral hydrodynamic invariants. J. Geom. Phys., 1992, 9(1), 101–110.
Tabachnikov S. L. Two remarks on the asymptotic Hopf invariant. Funct. Anal. Appl., 1990, 24(1), 74–75.
1976-5 — S. L. Tabachnikov
Tabachnikov S. L. Two remarks on the asymptotic Hopf invariant. Funct. Anal. Appl., 1990, 24(1), 74–75.
1976-6 — M. B. Mishustin
Mishustin M. B. Neighborhoods of the Riemann sphere in complex surfaces. Funct. Anal. Appl., 1993, 27(3), 176–185.
1976-8
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-9 — A. A. Davydov
Arnold V. I. Wave front evolution and equivariant Morse lemma. Commun. Pure Appl. Math., 1976, 29(6), 557–582; correction: 1977, 30(6), 823. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 289–318.]
Arnold V. I., Gusein-Zade S. M., Varchenko A. N. Singularities of Differentiable Maps, Vol. I: The Classification of Critical Points, Caustics and Wave Fronts. Boston, MA: Birkhäuser, 1985. (Monographs in Math., 82.) [The Russian original 1982.]
Bogaevsky I. A. Perestroikas of fronts in evolutionary families. Proc. Steklov Inst. Math., 1995, 209, 57–72.
Bressan A., Piccoli B. A generic classification of time-optimal planar stabilizing feedbacks. SIAM J. Control Optim., 1998, 36(1), 12–32.
Davydov A. A., Zakalyukin V. M. The coincidence of generic singularities of solutions of extremal problems with constraints. In: Proceedings of the International Conference Dedicated to the 90th Birthday of L. S. Pontryagin (Moscow, 1998), Vol. 3: Geometic Control Theory. Itogi Nauki i Tekhniki VINITI. Contemporary Mathematics and its Applications. Thematic Surveys, Vol. 64. Moscow: VINITI, 1999, 118–143 (in Russian).
Piccoli B. Classification of generic singularities for the planar time-optimal synthesis. SIAM J. Control Optimization, 1996, 34(6), 1914–1946.
Piccoli B. Regular time-optimal syntheses for smooth planar systems. Rend. Semin. Mat. Univ. Padova, 1996, 95, 59–79.
Piccoli B., Sussmann H. J. Regular synthesis and sufficient conditions for optimality. SIAM J. Control Optimization, 2000, 39(2), 359–410.
Zakalyukin V. M. Reconstructions of fronts and caustics depending on a parameter and versality of mappings. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics, Vol. 22. Moscow: VINITI, 1983, 56–93 (in Russian) [The English translation: J. Sov. Math., 1984, 27, 2713–2735.]
Zakalyukin V. M. Envelopes of families of wave fronts and control theory. Proc. Steklov Inst. Math., 1995, 209, 114–123.
1976-10
Arnold V. I. Some unsolved problems in the theory of differential equations. In: Unsolved Problems in Mechanics and Applied Mathematics. Moscow: Moscow University Press, 1977, 3–9 (in Russian).
1976-12
KhovanskiĬ A. G. Fewnomials. Providence, RI: Amer. Math. Soc., 1991. (Transl. Math. Monographs, 88.)
KhovanskiĬ A. G. Fewnomials. Moscow: PHASIS, 1997 (in Russian). (Mathematician's Library, 2.)
1976-12 — S. L. Tabachnikov
Itenberg I. V., Roy M. Multivariate Descartes’ rule. Beiträge zur Algebra und Geometrie, 1996, 37(2), 337–346.
Li T., Wang X. On multivariate Descartes’ rule—a counterexample. Beiträge zur Algebra und Geometrie, 1998, 39(1), 1–5.
Sturmfels B. Polynomial equations and convex polytopes. Amer. Math. Monthly, 1998,105(10), 907–922.
1976-13
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-14
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-15
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-16
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-17
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-18
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-19
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-20
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-21
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-22
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
Problems of present day mathematics. Editor: F. E. Browder. In: Mathematical Developments Arising from Hilbert Problems (Northern Illinois University, 1974). Part 1. Editor: F. E. Browder. Providence, RI: Amer. Math. Soc., 1976, 35–79. (Proc. Symposia Pure Math., 28.)
1976-22 — V. N. Karpushkin
Arnold V. I. Remarks on the stationary phase method and Coxeter numbers. Russian Math. Surveys, 1973, 28(5), 19–48.
Karpushkin V. N. Uniform estimates of oscillatory integrals with parabolic or hyperbolic phase. Trudy Semin. Petrovskogo, 1983, 9, 1–39 (in Russian). [The English translation: J. Sov. Math., 1986, 33, 1159–1188.]
Karpushkin V. N. A theorem concerning uniform estimates of oscillatory integrals when the phase is a function of two variables. Trudy Semin. Petrovskogo, 1984, 10, 150–169 (in Russian). [The English translation: J. Sov. Math., 1986, 35, 2809–2826.]
Karpushkin V. N. Dominant term in the asymptotics of oscillatory integrals with a phase of the series T. Math. Notes, 1994, 56(6), 1304–1305.
Karpushkin V. N. Uniform estimates of oscillatory integrals with phase from the series \(\tilde R_m \)Math. Notes, 1998, 64(3), 404–406.
Varchenko A. N. Newton polyhedra and estimation of oscillating integrals. Funct. Anal. Appl., 1976, 10(3), 175–196.
1976-23
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-24
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Problems of present day mathematics. Editor: F. E. Browder. In: Mathematical Developments Arising from Hilbert Problems (Northern Illinois University, 1974). Part 1. Editor: F. E. Browder. Providence, RI: Amer. Math. Soc., 1976, 35–79. (Proc. Symposia Pure Math., 28.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-25
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
Problems of present day mathematics. Editor: F. E. Browder. In: Mathematical Developments Arising from Hilbert Problems (Northern Illinois University, 1974). Part 1. Editor: F. E. Browder. Providence, RI: Amer. Math. Soc., 1976, 35–79. (Proc. Symposia Pure Math., 28.)
1976-26
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-27
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-28
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-29
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulas and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Problems of present day mathematics. Editor: F. E. Browder. In: Mathematical Developments Arising from Hilbert Problems (Northern Illinois University, 1974). Part 1. Editor: F. E. Browder. Providence, RI: Amer. Math. Soc., 1976, 35–79. (Proc. Symposia Pure Math., 28.)
Arnold V. I. Some problems in the theory of differential equations. In: Unsolved Problems of Mechanics and Applied Mathematics. Moscow: Moscow University Press, 1977, 3–9 (in Russian).
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-30
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-31
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulas and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Problems of present day mathematics. Editor: F. E. Browder. In: Mathematical Developments Arising from Hilbert Problems (Northern Illinois University, 1974). Part 1. Editor: F. E. Browder. Providence, RI: Amer. Math. Soc., 1976, 35–79. (Proc. Symposia Pure Math., 28.)
Arnold V. I. Some problems in the theory of differential equations. In: Unsolved Problems of Mechanics and Applied Mathematics. Moscow: Moscow University Press, 1977, 3–9 (in Russian).
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-32
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-33
Arnold V. I. Some open problems in the theory of singularities. In: The Theory of Cubature Formulae and Applications of Functional Analysis to Problems of Mathematical Physics. Editor: S. V. Uspenskiĭ. Novosibirsk: Press of the Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences, 1976, 5–15 (in Russian). (Trudy Seminara S. L. Soboleva, 1.)
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1976-34
Problems of present day mathematics. Editor: F. E. Browder. In: Mathematical Developments Arising from Hilbert Problems (Northern Illinois University, 1974). Part 1. Editor: F. E. Browder. Providence, RI: Amer. Math. Soc., 1976, 35–79. (Proc. Symposia Pure Math., 28.)
1976-35
Problems of present day mathematics. Editor: F. E. Browder. In: Mathematical Developments Arising from Hilbert Problems (Northern Illinois University, 1974). Part 1. Editor: F. E. Browder. Providence, RI: Amer. Math. Soc., 1976, 35–79. (Proc. Symposia Pure Math., 28.)
1976-35 — V. M. Kharlamov
Bihan F. Asymptotics of Betti numbers of real algebraic surfaces. Comment. Math. Helvetici, 2003, 78(2), 227–244.
Viro O. Ya. Construction of multicomponent real algebraic surfaces. Sov. Math. Dokl., 1979, 20, 991–995.
1976-36
Problems of present day mathematics. Editor: F. E. Browder. In: Mathematical Developments Arising from Hilbert Problems (Northern Illinois University, 1974). Part 1. Editor: F. E. Browder. Providence, RI: Amer. Math. Soc., 1976, 35–79. (Proc. Symposia Pure Math., 28.)
1976-36 — V. M. Kharlamov
Arnold V. I. Distribution of ovals of real plane algebraic curves, involutions of four-dimensional smooth manifolds, and the arithmetic of integral quadratic forms. Funct. Anal. Appl., 1971, 5(3), 169–176. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 175–187.]
Chevallier B. Four M-curves of degree 8. Funct. Anal. Appl., 2002, 36(1), 76–78.
Gudkov D. A. Complete topological classification of the disposition of ovals of a sixth order curve in the projective plane. Uchen. Zap. Gor'kov. Univ., 1969, 87, 118–153 (in Russian).
Gudkov D. A. Position of the circuits of a curve of sixth order. Sov. Math. Dokl, 1969, 10, 332–335.
Gudkov D. A. Construction of a new series of M-curves. Sov. Math. Dokl., 1971, 12, 1559–1563.
Itenberg I. V., Viro O. Ya. Patchworking algebraic curves disproves the Ragsdale conjecture. Math. Intelligencer, 1996, 18(4), 19–28. [Internet: http://www.math.uu.se/~oleg/preprints.html]
Kharlamov V. M., Orevkov S. Yu. Growth order of the number of classes of real plane algebraic curves as the degree grows. Zap. Nauch. Semin. St. Peterburg. Otdel. Mat. Inst. Steklova, 2000, 266, 218–233 (in Russian). (Theory of representations of dynamical systems. Combinatorial and algorithmic methods, 5.)
Ragsdale V. On the arrangement of the real branches of plane algebraic curves. Amer. J. Math., 1906, 28, 377–404.
Rokhlin V. A. Congruences modulo 16 in Hilbert's sixteenth problem. Funct. Anal. Appl., 1972, 6(4), 301–306.
Viro O. Ya. Curves of degree 7, curves of degree 8, and the Ragsdale conjecture. Sov. Math. Dokl., 1980, 22, 566–570.
1976-37
Problems of present day mathematics. Editor: F. E. Browder. In: Mathematical Developments Arising from Hilbert Problems (Northern Illinois University, 1974). Part 1. Editor: F. E. Browder. Providence, RI: Amer. Math. Soc., 1976, 35–79. (Proc. Symposia Pure Math., 28.)
Arnold V. I. Some problems in the theory of differential equations. In: Unsolved Problems of Mechanics and Applied Mathematics. Moscow: Moscow University Press, 1977, 3–9 (in Russian).
1976-37 — S. Yu. Yakovenko
Bautin N. N. On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type. AMS Transl., 1954, 100, 19 pp.
Ling S. S. A concrete example of the existence of four limit cycles for plane quadratic systems. Sci. Sinica, 1980, 23(2), 153–158.
Yakovenko S. A geometric proof of the Bautin theorem. In: Concerning the Hilbert 16th Problem. Editors: Yu. Il'yashenko and S. Yakovenko. Providence, RI: Amer. Math. Soc., 1995, 203–219. (AMS Transl., Ser. 2, 165; Adv. Math. Sci., 23.)
Żołądek H. Quadratic systems with center and their perturbations. J. Differ. Equations, 1994, 109(2), 223–273.
1976-38
Problems of present day mathematics. Editor: F. E. Browder. In: Mathematical Developments Arising from Hilbert Problems (Northern Illinois University, 1974). Part 1. Editor: F. E. Browder. Providence, RI: Amer. Math. Soc., 1976, 35–79. (Proc. Symposia Pure Math., 28.)
1976-39
Problems of present day mathematics. Editor: F. E. Browder. In: Mathematical Developments Arising from Hilbert Problems (Northern Illinois University, 1974). Part 1. Editor: F. E. Browder. Providence, RI: Amer. Math. Soc., 1976, 35–79. (Proc. Symposia Pure Math., 28.)
Arnold V. I. Some problems in the theory of differential equations. In: Unsolved Problems of Mechanics and Applied Mathematics. Moscow: Moscow University Press, 1977, 3–9 (in Russian).
Arnold V. I. Sur une propriété topologique des applications globalement canoniques de la mécanique classique. C. R. Acad. Sci. Paris, 1965, 261(19), 3719–3722.
The Russian translation in: [3b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 81–86.
1976-40
Problems of present day mathematics. Editor: F. E. Browder. In: Mathematical Developments Arising from Hilbert Problems (Northern Illinois University, 1974). Part 1. Editor: F. E. Browder. Providence, RI: Amer. Math. Soc., 1976, 35–79. (Proc. Symposia Pure Math., 28.)
1976-41
Arnold V. I. Some problems in the theory of differential equations. In: Unsolved Problems of Mechanics and Applied Mathematics. Moscow: Moscow University Press, 1977, 3–9 (in Russian).
1976-42
Arnold V. I. Some problems in the theory of differential equations. In: Unsolved Problems of Mechanics and Applied Mathematics. Moscow: Moscow University Press, 1977, 3–9 (in Russian).
1977-3 — V. V. Goryunov
Matov V. I. Singularities of the maximum function on a manifold with boundary. Trudy Semin. Petrovskogo, 1981, 6, 195–222 (in Russian). [The English translation: J. Sov. Math., 1986, 33, 1103–1127.]
Matov V. I. Unimodal and bimodal germs of functions on a manifold with boundary. Trudy Semin. Petrovskogo, 1981, 7, 174–189 (in Russian). [The English translation: J. Sov. Math., 1985, 31, 3193–3205.]
1977-4 — S. M. Gusein-Zade
Lyashko O. V. Classification of critical points of functions on a manifold with singular boundary. Funct. Anal. Appl., 1983, 17(3), 187–193.
1977-7 — S. M. Gusein-Zade
Ebeling W., Gusein-Zade S. M. On the index of a holomorphic 1-form on an isolated complete intersection singularity. Dokl. Math, 2001, 64(2), 221–224.
Ebeling W., Gusein-Zade S. M. Indices of 1-forms on an isolated complete intersection singularity. [Internet: http://www.arXiv.org/abs/math.AG/0105242]
1977-10 — V. V. Goryunov
Aleksandrov A. G. The de Rham complex of a quasihomogeneous complete intersection. Funct. Anal. Appl., 1983, 17(1), 48–49.
Aleksandrov A. G. Cohomology of a quasihomogeneous complete intersection. Math. USSR, Izv., 1986, 26, 437–477.
Arnold V. I. On some problems in singularity theory. In: Geometry and Analysis. Papers dedicated to the memory of V. K. Patodi. Bangalore: Indian Acad. Sci., 1980, 1–9. [Reprinted in: Proc. Indian Acad. Sci. Math. Sci., 1981, 90(1), 1–9.]
1977-12 — A. I. Neĭshtadt
Arnold V. I. Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields. Funct. Anal. Appl., 1977, 11(2), 85–92.
Arnold V. I. Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd edition. New York: Springer, 1988. (Grundlehren der Mathematischen Wissenschaften, 250.) [The Russian original 1978.]
Arnold V. I., AfraĬmovich V. S., Il'yashenko Yu. S., Shil'nikov L. P. Bifurcation theory. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics, Vol. 5. Moscow: VINITI, 1986, 5–218 (in Russian). [The English translation: Bifurcation Theory and Catastrophe Theory. Editor: V. I. Arnold. Berlin: Springer, 1994, 1–205. (Encyclopaedia Math. Sci., 5; Dynamical Systems, V.)]
Berezovskaya F. S., Khibnik A. I. On the problem of bifurcations of autooscillations near a 1:4 resonance. Preprint, Research Computing Center of the USSR Academy of Sciences, Pushchino, 1979 (in Russian).
Berezovskaya F. S., Khibnik A. I. On bifurcations of separatrices in the problem of loss of stability to auto-oscillations near a 1:4 resonance. J. Appl. Math. Mech., 1981, 44, 663–667.
Cheng Ch.-Q. Hopf bifurcations in nonautonomous systems at points of resonance. Science in China, Ser. A, 1990, 33(2), 206–219.
Cheng Ch.-Q., Sun Y.-S. Metamorphoses of phase portraits of vector field in the case of symmetry of order 4. J. Differ. Equations, 1992, 95(1), 130–139.
Chow S.-N., Li C., Wang D. Normal Forms and Bifurcation of Planar Vector Fields. Cambridge: Cambridge University Press, 1994.
Krauskopf B. Bifurcation sequences at 1: 4 resonance: an inventory. Nonlinearity, 1994, 7(3), 1073–1091.
NeĬshtadt A. I. Bifurcations of the phase portrait of a system of equations arising from the problem of loss stability of an auto-oscillations close to a 1: 4 resonance. J. Appl. Math. Mech., 1979, 42, 896–907.
Wan Y.-H. Bifurcation into invariant tori at points of resonance. Arch. Rat. Mech. Anal., 1978, 68(4), 343–357.
Wang D. Hopf bifurcation at the nonzero foci in 1: 4 resonance. Acta Math. Sinica (N. S.), 1990, 6(1), 10–17.
Zegeling A. Equivariant unfoldings in the case of symmetry of order 4. Serdica Math. J., 1993, 19(1), 71–79.
1978-2 — A. A. Davydov
Arnold V. I. Catastrophe theory. Berlin: Springer, 1992. [The Russian original 1990.]
Davydov A. A. The quasi-Hölder nature of the boundary of attainability. Trudy Semin. Vekt. Tenz. Anal., 1985, 22, 25–30 (in Russian). [The English translation: Selecta Math. Sov., 1990, 9(3), 229–234.]
Davydov A. A. Qualitative Theory of Control Systems. Providence, RI: Amer. Math. Soc., 1994. (Transl. Math. Monographs, 141.)
Davydov A. A., Zakalyukin V. M. The coincidence of generic singularities of solutions of extremal problems with constraints. In: Proceedings of the International Conference Dedicated to the 90th Birthday of L. S. Pontryagin (Moscow, 1998), Vol. 3: Geometic Control Theory. Itogi Nauki i Tekhniki VINITI. Contemporary Mathematics and its Applications. Thematic Surveys, Vol. 64. Moscow: VINITI, 1999, 118–143 (in Russian).
1978-3 — M. B. Sevryuk
Landis E. E. Uniform steepness indices. Uspekhi Mat. Nauk, 1986, 41(4), 179 (in Russian).
1978-6 — S. Yu. Yakovenko
Arnold V. I. Lectures on bifurcations and versal families. Russian Math. Surveys, 1972, 27(5), 119–184.
Arnold V. I. Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd edition. New York: Springer, 1988. (Grundlehren der Mathematischen Wissenschaften, 250.) [The Russian original 1978.]
Arnold V. I. Sur quelques problèmes de la théorie des systèmes dynamiques. Topol. Methods Nonlinear Anal., 1994, 4(2), 209–225. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 533–551.]
Arnold V. I., OleĬnik O. A. Topology of real algebraic varieties. Moscow Univ. Math. Bull., 1979, 34(6), 5–17.
Arnold V. I., Vishik M. I., Il'yashenko Yu. S., Kalashnikov A. S., Kondrat'ev V. A., Kruzhkov S. N., Landis E. M., Millionshchikov V. M., OleĬnik O. A., Filippov A. F., Shubin M. A. Some unsolved problems in the theory of differential equations and mathematical physics. Russian Math. Surveys, 1989, 44(4), 157–171. [The Russian original of the section “Problems by V. I. Arnold” (Uspekhi Mat. Nauk, 1989, 44(4), p. 191–192) is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 471–472.]
Bogdanov R. I. Bifurcations of the limit cycle of a family of plane vector fields. Trudy Semin. Petrovskogo, 1976, 2, 23–35. [The English translation: Selecta Math. Sov., 1981,1(4), 373–387.]
Bogdanov R. I. Versal deformation of a singularity point of a vector field on the plane in the case of zero eigenvalues. Trudy Semin. Petrovskogo, 1976, 2, 37–65 (in Russian). [The English translation: Selecta Math. Sov., 1981, 1(4), 389–421.]
Dulac H. Détermination et intégration d'une certaine classe d'équations différéntielles ayant pour point singulier un centre. Bull. Sci. Math. France, 1908, 32(2), 230–252.
Dumortier F., Roussarie R., Sotomayor J., Żolądek H. Bifurcations of planar vector fields. Nilpotent Singularities and Abelian Integrals. Berlin: Springer, 1991. (Lecture Notes in Math., 1480.)
Gavrilov L. Petrov modules and zeros of Abelian integrals. Bull. Sci. Math., 1998, 122(8), 571–584.
Gavrilov L. The infinitesimal 16th Hilbert problem in the quadratic case. Invent. Math., 2001, 143(3), 449–497.
Gavrilov L. Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians. Nonlinearity, 1998, 11(6), 1521–1537.
Glutsyuk A. A., Il'yashenko Yu. S. An estimate of the number of zeros of Abelian integrals for special Hamiltonians of arbitrary degree. [Internet: http://www.arXiv.org/abs/math.DS/0112156]
Il'yashenko Yu. S. The origin of limit cycles under perturbation of the equation dw/dz =-R z /R w , where R(z, w) is a polynomial. Math. USSR, Sb., 1969, 7, 353–364.
Il'yashenko Yu. S. The multiplicity of limit cycles arising from perturbations of the form dw/dz = P2/Q1 of a Hamilton equation, in the real and complex domain. Trudy Semin. Petrovskogo, 1978, 3, 49–60 (in Russian). [The English translation: AMS Transl., Ser. 2, 1982, 118, 191–202.]
Il'yashenko Yu. S., Yakovenko S. Yu. Double exponential estimate for the number of zeros of complete Abelian integrals and rational envelopes of linear ordinary differential equations with an irreducible monodromy group. Invent. Math., 1995, 121(3), 613–650.
Il'yashenko Yu. S., Yakovenko S. Yu. Counting real zeros of analytic functions satisfying linear ordinary differential equations. J. Differ. Equations, 1996, 126(1), 87–105.
KhovanskiĬ A. G. Real analytic varieties with the finiteness property and complex Abelian integrals. Funct. Anal. Appl., 1984, 18(2), 119–127.
KhovanskiĬ A. G. Fewnomials. Providence, RI: Amer. Math. Soc., 1991. (Transl. Math. Monographs, 88.)
KhovanskiĬ A. G. Fewnomials. Moscow: PHASIS, 1997 (in Russian). (Mathematician's Library, 2.)
Li Ch. AND Zhang Zh.-F. A criterion for determining the monotonicity of the ratio of two Abelian integrals. J. Differ. Equations, 1996, 124(2), 407–424.
Moussu R., Roche C. Théorie de Hovanskiĭ et problème de Dulac. Invent. Math., 1991, 105(2), 431–441.
Novikov D. I. Singular points of Picard-Fuchs systems, to appear.
Novikov D. I. Systems of linear ordinary differential equations with bounded coefficients may have very oscillating solutions. Proc. Amer. Math. Soc., 2001, 129(12), 3753–3755 (electronic).
Novikov D. I., Yakovenko S. Yu. Simple exponential estimate for the number of real zeros of complete Abelian integrals. C. R. Acad. Sci. Paris, Sér. I Math., 1995, 320(7), 853–858.
Novikov D. I., Yakovenko S. Yu. Simple exponential estimate for the number of real zeros of complete Abelian integrals. Ann. Inst. Fourier (Grenoble), 1995, 45(4), 897–927.
Novikov D. I., Yakovenko S. Yu. Meandering of trajectories of polynomial vector fields in the affine n-space. Publ. Mat., 1997, 41(1), 223–242.
Novikov D. I., Yakovenko S. Yu. Tangential Hilbert problem for perturbations of hyperelliptic Hamiltonian systems. Electron. Res. Announc. Amer. Math. Soc., 1999, 5, 55–65 (electronic).
Novikov D. I., Yakovenko S. Yu. Trajectories of polynomial vector fields and ascending chains of polynomial ideals. Ann. Inst. Fourier (Grenoble), 1999, 49(2), 563–609.
Novikov D. I., Yakovenko S. Yu. Redundant Picard-Fuchs system for Abelian integrals. J. Differ. Equations, 2001, 177(2), 267–306.
Petrov G. S. Elliptic integrals and their nonoscillation. Funct. Anal. Appl., 1986, 20(1), 37–40.
Petrov G. S. The Chebyshev property of elliptic integrals. Funct. Anal. Appl., 1988, 22(1), 72–73.
PetrovskiĬ I. G., Landis E. M. On the number of limit cycles of the equation dy/dx = M(x,y)/N(x,y), where the M and N are polynomials of second degree. Dokl. Akad. Nauk SSSR (N.S.), 1955, 102, 29–32 (in Russian). [The English translation: AMS Transl., Ser. 2, 1958, 10, 177–221.]
PetrovskiĬ I. G., Landis E. M. On the number of limit cycles of the equation dy/dx = P(x,y)/Q(x,y), where P and Q are polynomials of degree n. Dokl. Akad. Nauk SSSR (N. S.), 1957, 113, 748–751 (in Russian). [The English translation: AMS Transl, Ser. 2, 1960, 14, 181–199.]
PetrovskiĬ I. G., Landis E. M. Corrections to the articles “On the number of limit cycles of the equations dy/dx = P(x, y)/Q(x, y), where P and Q are polynomials of 2nd degree” and “On the number of limit cycles of the equation dy/dx = P(x, y)/Q(x, y), where P and Q are polynomials.” Mat. Sb. (N. S.), 1959 48(90), 253–255 (in Russian).
Pushkar' I. A. Multidimensional generalization of the Il'yashenko theorem on Abelian integrals. Funct. Anal. Appl., 1997, 31(2), 100–108.
Roussarie R. On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields. Bol. Soc. Brasil. Mat., 1986, 17(2), 67–101.
Roussarie R. Cyclicité finie des lacets et des points cuspidaux. Nonlinearity, 1989, 2(1), 73–117.
Takens F. Forced oscillations and bifurcations. In: Applications of Global Analysis, I (Utrecht, 1973). Preprint, Utrecht: Math. Inst. Rijksuniv. Utrecht, 1974, 1–59. (Comm. Math. Inst. Rijksuniv. Utrecht, 3-1974.) [Published in: Global Analysis of Dynamical Systems. Festschrift dedicated to Floris Takens for his 60th birthday. Editors: H. W. Broer, B. Krauskopf and G. Vegter. Bristol: Inst. Phys., 2001, 1–61.]
Varchenko A. N. Estimate of the number of zeros of an Abelian integral depending on a parameter, and limit cycles. Funct. Anal. Appl., 1984, 18(2), 98–108.
Yakovenko S. Yu. Quantitative theory of ordinary differential equations and tangential Hilbert 16th problem. Lecture notes of the course delivered at the Workshop “Asymptotic series, differential algebra and finiteness theorems” (Montreal, 2000). [Internet: http://www.arXiv.org/abs/math.DS/0104140]
Żołądek H. Quadratic systems with center and their perturbations. J. Differ. Equations, 1994, 109(2), 223–273.
1978-7 — A. I. Neĭshtadt, M. B. Sevryuk
Arnold V. I., Kozlov V. V., NeĬshtadt A. I. Mathematical Aspects of Classical and Celestial Mechanics, 2nd edition. Berlin: Springer, 1993, Ch. 7, §3. (Encyclopædia Math. Sci., 3; Dynamical systems, III.) [The Russian original 1985.] [The second, revised and supplemented, Russian edition 2002.]
Braaksma B. L. J., Broer H. W. On a quasi-periodic Hopf bifurcation. Ann. Institut Henri Poincaré, Analyse non linéaire, 1987, 4(2), 115–168.
Braaksma B. L. J., Broer H. W., Huitema G. B. Towards a quasi-periodic bifurcation theory. Mem. Amer. Math. Soc., 1990, 83(421), 83–170.
Broer H. W. On some quasi-periodic bifurcations. Delft Progress Report, 1988, 12(1), 79–96.
Broer H. W., Huitema G. B., Sevryuk M. B. Quasi-Periodic Motions in Families of Dynamical Systems: Order amidst Chaos. Berlin: Springer, 1996, Sect. 4.3. (Lecture Notes in Math., 1645.)
Bruno A. D. The Restricted 3-Body Problem: Plane Periodic Orbits. Berlin: Walter de Gruyter, 1994. [The Russian original 1990.]
Duistermaat J. J. Bifurcations of periodic solutions near equilibrium points of Hamiltonian systems. In: Bifurcation Theory and Applications. Editor: L. Salvadori. Berlin: Springer, 1984, 57–105. (Lecture Notes in Math., 1057.)
Haller G. Chaos near Resonance. New York: Springer, 1999, Sect. 4.1. (Appl. Math. Sci., 138.)
Haller G., Wiggins S. Whiskered tori and chaos in resonant Hamiltonian normal forms. In: Normal Forms and Homoclinic Chaos. Editors: W. F. Langford and W. Nagata. Providence, RI: Amer. Math. Soc., 1995, 129–149. (Fields Institute Commun., 4.)
Haller G., Wiggins S. Geometry and chaos near resonant equilibria of 3-DOF Hamiltonian systems. Physica D, 1996, 90(4), 319–365.
Hanssmann H. The quasi-periodic centre-saddle bifurcation. J. Differ. Equations, 1998, 142(2), 305–370.
Henrard J. Periodic orbits emanating from a resonant equilibrium. Celest. Mech., 1970, 1(3/4), 437–466.
Hoveijn I. Aspects of resonance in dynamical systems. Ph. D. Thesis, University of Utrecht, 1992.
Joyeux M. Classical dynamics of the 1: 1, 1: 2 and 1: 3 resonance Hamiltonians. Chem. Physics, 1996, 203(3), 281–307.
Schmidt D. S. Periodic solutions near a resonant equilibrium of a Hamiltonian system. Celest. Mech., 1974, 9(1), 81–103.
Sevryuk M. B. Reversible Systems. Berlin: Springer, 1986. (Lecture Notes in Math., 1211.)
Sevryuk M. B. Reversible dynamical systems. Ph. D. Thesis, Moscow State University, 1987 (in Russian).
Wiggins S. Phase space geometry and dynamics associated with the 1: 2: 2 resonance. In: Hamiltonian Systems with Three or More Degrees of Freedom (S'Agaró, 1995). Editor: C. Simó. Dordrecht: Kluwer Acad. Publ., 1999, 254–269. (NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 533.)
1978-10 — V. V. Goryunov
Arnold V. I. Singularities of Caustics and Wave Fronts. Dordrecht: Kluwer Academic Publ., 1990, Sect. 6.1. (Math. Appl., Sov. Ser., 62.)
Landis E. E. Tangential singularities. Funct. Anal. Appl., 1981, 15(2), 103–114.
Platonova O. A. Projections of smooth surfaces. Trudy Semin. Petrovskogo, 1984, 10, 135–149 (in Russian). [The English translation: J. Sov. Math., 1986, 35, 2796–2808.]
1978-17 — I. A. Bogaevsky
Arnold V. I. On the interior scattering of waves, defined by hyperbolic variational principles. J. Geom. Phys., 1988, 5(3), 305–315.
Arnold V. I. Surfaces defined by hyperbolic equations. Math. Notes, 1988, 44(1), 489–497. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 397–412.]
Arnold V. I. Singularities of Caustics and Wave Fronts. Dordrecht: Kluwer Acad. Publ., 1990. (Math. Appl., Sov. Ser., 62.)
Arnold V. I. Singularities of Caustics and Wave Fronts. Moscow: PHASIS, 1996 (in Russian). (Mathematician's Library, 1.)
Bogaevsky I. A. Singularities of the propagation of short waves on the plane. Sb. Math., 1995, 186(11), 1581–1597.
Bogaevsky I. A. The interior scattering of rays and wave fronts on the plane. In: ARNOLD V. I. Singularities of Caustics and Wave Fronts. Moscow: PHASIS, 1996, § 8.5, 300–316 (in Russian).
Bogaevsky I. A. Singularities of short linear waves on the plane. In: The Arnold-Gelfand Mathematical Seminars: Geometry and Singularity Theory. Editors: V. I. Arnold, I. M. Gelfand, V. S. Retakh and M. Smirnov. Boston, MA: Birkhäuser, 1997, 107–112.
Braam P. J., Duistermaat J. J. Normal forms of real symmetric systems with multiplicity. Indag. Math. (N. S.), 1993, 4(4), 407–421.
Khesin B. A. Singularities of light hypersurfaces and structure of hyperbolicity sets for systems of partial differential equations. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 119–127. (Adv. Sov. Math., 1.)
1978-19
Bakhtin V. I. Topologically normal forms of caustic transformations of Dµ-series. Moscow Univ. Math. Bull., 1987, 42(4), 63–66.
1979-4 — B. A. Khesin
Khesin B. A., Rosly A. A. Polar homology. [Internet: http://www.arXiv.org/abs/math.AG/0009015]
Khesin B. A., Rosly A. A. Polar homology and holomorphic bundles. Phil. Trans. Roy. Soc. London, Ser. A, 2001, 359, 1413–1427.
Khesin B. A., Rosly A. A. Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces. In: The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (Toronto, 1997). Editors: E. Bierstone, B. A. Khesin, A. G. Khovanskiĭ and J. E. Marsden. Providence, RI: Amer. Math. Soc., 1999, 311–323. (Fields Inst. Commun., 24.)
1979-6 — V. A. Vassiliev
Vassiliev V. A., Serganova V. V. On the number of real and complex moduli of singularities of smooth functions and matroid realizations. Math. Notes, 1991, 49(1), 15–20.
Gabrielov A. M. Bifurcations, Dynkin diagrams, and modality of isolated singularities. Funct. Anal. Appl., 1974, 8(2), 94–98.
1979-8 — V. A. Vassiliev
Gabrielov A. M. Bifurcations, Dynkin diagrams, and modality of isolated singularities. Funct. Anal. Appl., 1974, 8(2), 94–98.
1979-14 — A. A. Davydov
Bogaevsky I. A. Perestroikas of fronts in evolutionary families. Proc. Steklov Inst. Math., 1995, 209, 57–72.
Bryzgalova L. N. Singularities of the maximum of a parametrically dependent function. Funct. Anal. Appl., 1977, 11(1), 49–51.
Bryzgalova L. N. Maximum functions of a family of functions depending on parameters. Funct. Anal. Appl., 1978, 12(1), 50–51.
Davydov A. A. Local controllability of typical dynamic inequalities on surfaces. Proc. Steklov Inst. Math., 1995, 209, 73–106.
Davydov A. A., Zakalyukin V. M. Point singularities of the conditional minimum on a three-dimensional manifold. Proc. Steklov Inst. Math., 1998, 220, 109–125.
Davydov A. A., Zakalyukin V. M. The coincidence of generic singularities of solutions of extremal problems with constraints. In: Proceedings of the International Conference Dedicated to the 90th Birthday of L. S.Pontryagin (Moscow, 1998), Vol. 3: Geometic Control Theory. Itogi Nauki i Tekhniki VINITI. Contemporary Mathematics and its Applications. Thematic Surveys, Vol. 64. Moscow: VINITI, 1999, 118–143 (in Russian).
Matov V. I. The topological classification of germs of the maximum and minimax functions of a family of functions in general position. Russian Math. Surveys, 1982, 37(4), 127–128.
1979-16
Arnold V. I., OleĬnik O. A. Topology of real algebraic varieties. Vestnik Moskov. Univ. Ser. Mat. Mekh., 1979, № 6, 7–17 (in Russian). [The English translation: Moscow Univ. Math. Bull., 1979, 34(6), 5–17.]
1979-17
Arnold V. I., OleĬnik O. A. Topology of real algebraic varieties. Vestnik Moskov. Univ. Ser. Mat. Mekh., 1979, № 6, 7–17 (in Russian). [The English translation: Moscow Univ. Math. Bull., 1979, 34(6), 5–17.]
1979-17 — V. M. Kharlamov
Kharlamov V. M., Orevkov S. Yu. Growth order of the number of classes of real plane algebraic curves as the degree grows. Zap. Nauch. Semin. St. Peterburg. Otdel. Mat. Inst. Steklova, 2000, 266, 218–233 (in Russian). (Theory of representations of dynamical systems. Combinatorial and algorithmic methods, 5.)
Nabutovsky A. Nonrecursive functions in real algebraic geometry. Bull. Amer. Math. Soc. (N. S.), 1989, 20(1), 61–65.
Nabutovsky A. Disconnectedness of sublevel sets of some Riemannian functionals. Geom. Funct. Anal., 1996, 6(4), 703–725.
Nabutovsky A. Geometry of the space of triangulations of a compact manifold. Commun. Math. Phys., 1996, 181(2), 303–330.
Nuij W. A note on hyperbolic polynomials. Math. Scand., 1968, 23, 69–72.
1979-18
Arnold V. I., OleĬnik O. A. Topology of real algebraic varieties. Vestnik Moskov. Univ. Ser. Mat. Mekh., 1979, № 6, 7–17 (in Russian). [The English translation: Moscow Univ. Math. Bull., 1979, 34(6), 5–17.]
1979-19
Arnold V. I., OleĬnik O. A. Topology of real algebraic varieties. Vestnik Moskov. Univ. Ser. Mat. Mekh., 1979, № 6, 7–17 (in Russian). [The English translation: Moscow Univ. Math. Bull., 1979, 34(6), 5–17.]
1979-19 — S. L. Tabachnikov
Itenberg I. V., Viro O. Ya. Patchworking algebraic curves disproves the Ragsdale conjecture. Math. Intelligencer, 1996, 18(4), 19–28. [Internet: http://www.math.uu.se/~oleg/preprints.html]
1979-20
Arnold V. I., OleĬnik O. A. Topology of real algebraic varieties. Vestnik Moskov. Univ. Ser. Mat. Mekh., 1979, № 6, 7–17 (in Russian). [The English translation: Moscow Univ. Math. Bull., 1979, 34(6), 5–17.]
1979-21
Arnold V. I., OleĬnik O. A. Topology of real algebraic varieties. Vestnik Moskov. Univ. Ser. Mat. Mekh., 1979, № 6, 7–17 (in Russian). [The English translation: Moscow Univ. Math. Bull., 1979, 34(6), 5–17.]
1979-22
Arnold V. I., OleĬnik O. A. Topology of real algebraic varieties. Vestnik Moskov. Univ. Ser. Mat. Mekh., 1979, № 6, 7–17 (in Russian). [The English translation: Moscow Univ. Math. Bull., 1979, 34(6), 5–17.]
1979-22 — S. Yu. Yakovenko
KhovanskiĬ A. G. Fewnomials. Providence, RI: Amer. Math. Soc., 1991. (Transl. Math. Monographs, 88.)
1979-23
Arnold V. I., OleĬnik O. A. Topology of real algebraic varieties. Vestnik Moskov. Univ. Ser. Mat. Mekh., 1979, № 6, 7–17 (in Russian). [The English translation: Moscow Univ. Math. Bull., 1979, 34(6), 5–17.]
1979-24
Arnold V. I., OleĬnik O. A. Topology of real algebraic varieties. Vestnik Moskov. Univ. Ser. Mat. Mekh., 1979, № 6, 7–17 (in Russian). [The English translation: Moscow Univ. Math. Bull., 1979, 34(6), 5–17.]
1979-24 — V. M. Kharlamov
Fiedler T. New congruences in the topology of real plane algebraic curves. Sov. Math. Dokl., 1983, 27, 566–568.
Marin A. ℂP2/σ ou Kuiper et Massey au pays des coniques. In: A la recherche de la topologie perdue. I. Le côté de chez Rohlin. II. Le côté de Casson. Editors: L. Guillou and A. Marin. Boston, MA — Basel — Stuttgart: Birkhäuser, 1986, 141–152. (Progr. Math., 62.)
Welschinger J. Y. Courbes algèbriques réelles et courbes flexibles sur les surfaces réglées de base ℂP1. Proc. London Math. Soc., Ser. 3, 2002, 85(2), 367–392.
1979-25
Arnold V. I., OleĬnik O. A. Topology of real algebraic varieties. Vestnik Moskov. Univ. Ser. Mat. Mekk, 1979, №6, 7–17 (in Russian). [The English translation: Moscow Univ. Math. Bull., 1979, 34(6), 5–17.]
1979-26
Arnold V. I., OleĬnik O. A. Topology of real algebraic varieties. Vestnik Moskov. Univ. Ser. Mat. Mekh., 1979, № 6, 7–17 (in Russian). [The English translation: Moscow Univ. Math. Bull., 1979, 34(6), 5–17.]
1979-26 — S. Yu. Yakovenko
Chow Sh.-N., Li Ch., Yi Y. The cyclicity of period annuli of degenerate quadratic Hamiltonian systems with elliptic segment loops. Ergod. Theory Dynam. Systems, 2002, 22(2), 349–374.
Gavrilov L. The infinitesimal 16th Hilbert problem in the quadratic case. Invent. Math., 2001, 143(3), 449–497.
Horozov E., Iliev I. D. On the number of limit cycles in perturbations of quadratic Hamiltonian systems. Proc. London Math. Soc., Ser. 3, 1994, 69(1), 198–224.
Li Ch., Zhang Z. Weak Hilbert problem for n = 2. Preprint, February 2002.
Markov Y. Limit cycles of perturbations of a class of quadratic Hamiltonian vector fields. Serdica Math. J., 1996, 22(2), 91–108.
Zhang Zh., Li Ch. On the number of limit cycles of a class of quadratic Hamiltonian systems under quadratic perturbations. Adv. Math. (China), 1997, 26(5), 445–460.
1979-27
Arnold V. I., OleĬnik O. A. Topology of real algebraic varieties. Vestnik Moskov. Univ. Ser. Mat. Mekh., 1979, № 6, 7–17 (in Russian). [The English translation: Moscow Univ. Math. Bull., 1979, 34(6), 5–17.]
1979-27 — S. Yu. Yakovenko
Bogdanov R. I. Versal deformation of a singularity point of a vector field on the plane in the case of zero eigenvalues. Trudy Semin. Petrovskogo, 1976, 2, 37–65 (in Russian). [The English translation: Selecta Math. Sov., 1981, 1(4), 389–421.]
Concerning the Hilbert 16th Problem. Editors: Yu. Il'yashenko and S. Yakovenko. Providence, RI: Amer. Math. Soc., 1995. (AMS Transl., Ser. 2, 165; Adv. Math. Sci., 23.)
Dumortier F., Roussarie R., Sotomayor J. Bifurcations of cuspidal loops. Nonlinearity, 1997, 10(6), 1369–1408.
Il'yashenko Yu. S., Kaloshin V. Yu. Bifurcation of planar and spatial polycycles: Arnold's program and its development. In: The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (Toronto, 1997). Editors: E. Bierstone, B. A. Khesin, A. G. Khovanskiĭ and J. E. Marsden. Providence, RI: Amer. Math. Soc., 1999, 241–271. (Fields Inst. Commun., 24.)
Il'yashenko Yu. S., Yakovenko S. Yu. Finite cyclicity of elementary polycycles in generic families. In: Concerning the Hilbert 16th Problem. Editors: Yu. Il'yashenko and S. Yakovenko. Providence, RI: Amer. Math. Soc., 1995, 21–95. (AMS Transl., Ser. 2, 165; Adv. Math. Sci., 23.)
Kaloshin V. Yu. Around Hilbert-Arnold problem. [Internet: http://www.arXiv.org/abs/math.DS/0111053]
Kaloshin V. Yu. The Hilbert-Arnold problem and an estimate of the cyclicity of polycycles of the plane and in space. Funct. Anal. Appl., 2001, 35(2), 146–147.
1980-2 — S. Yu. Yakovenko
Blinov M., Yomdin Y. Center and composition conditions for Abel differential equation, and rational curves. Qualit. Theory Dynam. Systems, 2001, 2(1), 111–127.
Briskin M., Françoise J.-P., Yomdin Y. Center conditions, compositions of polynomials and moments on algebraic curves. Ergod. Theory Dynam. Systems, 1999, 19(5), 1201–1220.
Ershov E. K. On the number of cycles of some differential equations on a two-dimensional torus. Differ. Uravneniya, 1991, 27(12), 2167–2169, 2207 (in Russian).
Françoise J.-P., Yomdin Y. Bernstein inequalities and applications to analytic geometry and differential equations. J. Funct. Anal., 1997, 146(1), 185–205.
Il'yashenko Yu. S. Hilbert-type numbers for Abel equations, growth and zeros of holomorphic functions. Nonlinearity, 2000, 13(4), 1337–1342.
Lins Neto A. On the number of solutions of the equation dx/dt = Σ nj=0 aj(t)xj, 0 ≤ t ≤ 1, for which x(0) = x(1). Invent. Math., 1980, 59(1), 67–76.
Panov A. A. The number of periodic solutions of polynomial differential equations. Math. Notes, 1998, 64(5), 622–628.
Panov A. A. On the diversity of Poincaré mappings for cubic equations with variable coefficients. Funct. Anal. Appl., 1999, 33(4), 310–312.
Shahshahani S. Periodic solutions of polynomial first order differential equations. Nonlinear Anal., 1981, 5(2), 157–165.
Yomdin Y. Global finiteness properties of analytic families and algebra of their Taylor coefficients. In: The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (Toronto, 1997). Editors: E. Bierstone, B. A. Khesin, A. G. Khovanskiĭ and J. E. Marsden. Providence, RI: Amer. Math. Soc., 1999, 527–555. (Fields Inst. Commun., 24.)
1980-3 — S. Yu. Yakovenko
Żoładek H. Quadratic systems with center and their perturbations. J. Differ. Equations, 1994, 109(2), 223–273.
1980-4 — M. B. Sevryuk
Arnold V. I. Reversible systems. In: Nonlinear and Turbulent Processes in Physics (Kiev, 1983), V. 3. Editor: R. Z. Sagdeev. Chur: Harwood Acad. Publ., 1984, 1161–1174. [For the Russian translation see, e.g.: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 355–363.]
Arnold V. I., Sevryuk M. B. Oscillations and bifurcations in reversible systems. In: Nonlinear Phenomena in Plasma Physics and Hydrodynamics. Editor: R. Z. Sagdeev. Moscow: Mir, 1986, 31–64.
Bunov A. V., Demëkhin E. A., Shkadov V. Ya. On the non-uniqueness of nonlinear wave solutions in a viscous layer. J. Appl. Math. Mech., 1984, 48(4), 495–499.
Demëkhin E. A. Branching of a solution of the problem on stationary traveling waves in a layer of viscous liquid on an inclined plane. Izvestiya Akad. Nauk SSSR, Ser. Mekh. Zhidkosti i Gaza (Mech. Liquid and Gas), 1983, 5, 36–44 (in Russian).
Devaney R. L. Reversible diffeomorphisms and flows. Trans. Amer. Math. Soc., 1976, 218, 89–113.
Furter J. E. On the bifurcations of subharmonics in reversible systems. In: Singularity Theory and its Applications, Part II. Editors: M. Roberts and I. Stewart. Berlin: Springer, 1991, 167–192. (Lecture Notes in Math., 1463.)
Gervais J.-J. Bifurcations of subharmonic solutions in reversible systems. J. Differ. Equations, 1988, 75(1), 28–42; addendum: 1989, 78(2), 400.
NepomnyashchiĬ A. A. Stability of wave regimes in a film flowing down on an inclined plane. Izvestiya Akad. Nauk SSSR, Ser. Mekh. Zhidkosti i Gaza (Mech. Liquid and Gas), 1974, 3, 28–34 (in Russian).
Sevryuk M. B. Reversible Systems. Berlin: Springer, 1986, §5.4. (Lecture Notes in Math., 1211.)
Vanderbauwhede A. Bifurcation of subharmonic solutions in time-reversible systems. Z. Angew. Math. Phys., 1986, 37(4), 455–478.
Vanderbauwhede A. Subharmonic branching in reversible systems. SIAM J. Math. Anal., 1990, 21(4), 954–979.
Vanderbauwhede A. Branching of periodic solutions in time-reversible systems. In: Geometry and Analysis in Nonlinear Dynamics. Editors: H. W. Broer and F. Takens. Harlow: Longman, 1992, 97–113. (Pitman Research Notes Math. Ser., 222.)
1980-9
Arnold V. I. On some problems in singularity theory. In: Geometry and Analysis. Papers dedicated to the memory of V. K. Patodi. Bangalore: Indian Acad. Sci., 1980, 1–9. [Reprinted in: Proc. Indian Acad. Sci. Math. Sci., 1981, 90(1), 1–9.]
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1980-9 — S. V. Chmutov
Arnold V. I. The index of a singular point of a vector field, the Petrovskiĭ-Oleĭnik inequalities, and mixed Hodge structures. Funct. Anal. Appl., 1978, 12(1), 1–12.
Kharlamov V. M. A generalized Petrovskiĭ inequality, I; II. Funct. Anal. Appl., 1974, 8(2), 132–137; 1975, 9(3), 266–268.
1980-11
Arnold V. I. On some problems in singularity theory. In: Geometry and Analysis. Papers dedicated to the memory of V. K. Patodi. Bangalore: Indian Acad. Sci., 1980, 1–9. [Reprinted in: Proc. Indian Acad. Sci. Math. Sci., 1981, 90(1), 1–9.]
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1980-11 — S. V. Chmutov
Arnold V. I., Vassiliev V. A., Goryunov V. V., Lyashko O. V. Singularities. I. Local and Global Theory. Berlin: Springer, 1993. (Encyclopædia Math. Sci., 6; Dynamical Systems, VI.) [The Russian original 1988.]
Steenbrink J. H. M. Semicontinuity of the singularity spectrum. Invent. Math., 1985, 79(3), 557–565.
Varchenko A. N. Asymptotic integrals and Hodge structures. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics, Vol. 22. Moscow: VINITI, 1983, 130–166 (in Russian). [The English translation: J. Sov. Math., 1984, 27, 2760–2784.]
Varchenko A. N. Semicontinuity of the complex singularity exponent. Funct. Anal. Appl., 1983, 17(4), 307–309.
Varchenko A. N. On semicontinuity of the spectrum and an upper estimate for the number of singular points of a projective hypersurface. Sov. Math. Dokl., 1983, 27, 735–739.
1980-14
Arnold V. I. On some problems in singularity theory. In: Geometry and Analysis. Papers dedicated to the memory of V. K. Patodi. Bangalore: Indian Acad. Sci., 1980, 1–9. [Reprinted in: Proc. Indian Acad. Sci. Math. Sci., 1981, 90(1), 1–9.]
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1980-15
Arnold V. I. On some problems in singularity theory. In: Geometry and Analysis. Papers dedicated to the memory of V. K. Patodi. Bangalore: Indian Acad. Sci., 1980, 1–9. [Reprinted in: Proc. Indian Acad. Sci. Math. Sci., 1981, 90(1), 1–9.]
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1980-15 — V. A. Vassiliev
Vassiliev V. A. Topology of complements to discriminants and loop spaces. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 9–21 (Adv. Sov. Math., 1.)
Vassiliev V. A. Complements of Discriminants of Smooth Maps: Topology and Applications, revised edition. Providence, RI: Amer. Math. Soc., 1994. (Transl. Math. Monographs, 98.)
1980-16
Arnold V. I. On some problems in singularity theory. In: Geometry and Analysis. Papers dedicated to the memory of V. K. Patodi. Bangalore: Indian Acad. Sci., 1980, 1–9. [Reprinted in: Proc. Indian Acad. Sci. Math. Sci., 1981, 90(1), 1–9.]
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1980-17
Arnold V. I. On some problems in singularity theory. In: Geometry and Analysis. Papers dedicated to the memory of V. K. Patodi. Bangalore: Indian Acad. Sci., 1980, 1–9. [Reprinted in: Proc. Indian Acad. Sci. Math. Sci., 1981, 90(1), 1–9.]
Arnold V. I. Some open problems in the theory of singularities. In: Singularities. Part 1 (Arcata, CA, 1981). Editor: P. Orlik. Providence, RI: Amer. Math. Soc., 1983, 57–69. (Proc. Symposia Pure Math., 40.)
1981-1 — M. B. Sevryuk
Coxeter H. S. M., Whitrow G. J. World-structure and non-Euclidean honeycombs. Proc. Roy. Soc. London, Ser. A, 1950, 201, 417–437.
Lannér F. On complexes with transitive groups of automorphisms. Commun. Sém. Math. Univ. Lund, 1950, 11, 71 pp.
1981-2 — N. N. Nekhoroshev
Il'yashenko Yu. S. A steepness criterion for analytic functions. Russian Math. Surveys, 1986, 41(1), 229–230.
Landis E. E. Uniform steepness indices. Uspekhi Mat. Nauk, 1986, 41(4), 179 (in Russian).
Nekhoroshev N. N. Stable lower estimates for smooth mappings and for gradients of smooth functions. Math. USSR, Sb., 1973, 19(3), 425–467.
Nekhoroshev N. N. An exponential estimate of the time of stability of nearly-integrable Hamiltonian systems. Russian Math. Surveys, 1977, 32(6), 1–65.
1981-3 — D. A. Popov
Arnold V. I., Gusein-Zade S. M., Varchenko A. N. Singularities of Differentiable Maps, Vol. II: Monodromy and Asymptotics of Integrals. Boston, MA: Birkhäuser, 1988. (Monographs in Math., 83.) [The Russian original 1984.]
Colin de Verdière Y. Nombre de points entiers dans une famille homothétique de domaines de \(\mathbb{R}^n \). Ann. Sci. École Norm. Sup., Sér. 4, 1977, 10(4), 559–575.
Popov D. A. Estimates with constants for some classes of oscillatory integrals. Russian Math. Surveys, 1997, 52(1), 73–145.
1981-4 — E. Ferrand
Gromov M. L. Pseudo holomorphic curves in symplectic manifolds. Invent. Math., 1985, 82(2), 307–347.
1981-6 — V. A. Vassiliev
Arnold V. I. Lagrange and Legendre cobordisms, I; II. Funct. Anal. Appl., 1980, 14(3), 167–177; 14(4), 252–260.
Audin M. Cobordismes d'immersions lagrangiennes et legendriennes. Paris: Hermann, 1987. (Travaux en Cours, 20.)
Eliashberg Ya. M. Cobordisme des solutions de relations différentielles. In: Séminaire Sud-Rhodanien de Géométrie. I (Lyon, 1983). Editors: P. Dazord and N. Desolneux-Moulis. Paris: Hermann, 1984, 17–31. (Travaux en Cours.)
Smith L., Stong R. E. Exotic cobordism theories associated with classical groups. J. Math. Mech., 1968, 17(12), 1087–1102.
1981-7 — E. Ferrand
Damian M. Homologie de Novikov et applications en topologie symplectique. Thèse, École Polytechnique, Palaiseau, France, 1999.
Hofer H. Lagrangian embeddings and critical point theory. Ann. Institut Henri Poincaré, Analyse non linéaire, 1985, 2(6), 465–499.
Laudenbach F., Sikorav J.-C. Persistance d'intersection avec la section nulle au cours d'une isotopie hamiltonienne dans un fibré cotangent. Invent. Math., 1985, 82(2), 349–357.
1981-8 — E. Ferrand
Pushkar' P. E. Relative Morse theory. Preprint, 1999.
1981-9 — V. L. Ginzburg
Arnold V. I. Some remarks on flows of line elements and frames. Sov. Math. Dokl., 1961, 2, 562–564.
Arnold V. I. On some problems in symplectic topology. In: Topology and Geometry. Rohlin Seminar. Editor: O. Ya. Viro. Berlin: Springer, 1988, 1–5. (Lecture Notes in Math., 1346.) [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 425–429.]
Arnold V. I. Remarks concerning the Morse theory of a divergence-free vector field, the averaging method, and the motion of a charged particle in a magnetic field. Proc. Steklov Inst. Math., 1997, 216, 3–13.
Benettin G., Sempio P. Adiabatic invariants and trapping of a point charge in a strong non-uniform magnetic field. Nonlinearity, 1994, 7(1), 281–303.
Bialy M. Rigidity for periodic magnetic fields, Ergod. Theory Dynam. Systems, 2000, 20(6), 1619–1626.
Castilho C. The motion of a charged particle on a Riemannian surface under a non-zero magnetic field. J. Differ. Equations, 2001, 171(1), 110–131.
Conley C. C., Zehnder E. Birkhoff-Lewis fixed point theorem and a conjecture of V. I. Arnold. Invent. Math., 1983, 73(1), 33–49.
Contreras G., Iturriaga R., Paternain G. P., Paternain M. Lagrangian graphs, minimizing measures and Mañe's critical value. Geom. Funct. Anal., 1998, 8(5), 788–809.
Contreras G., Iturriaga R., Paternain G. P., Paternain M. The Palais-Smale condition and Mañe's critical values. Ann. Henri Poincaré, 2000, 1(4), 655–684.
Contreras G., Iturriaga L., Paternain G. P. Periodic orbits for exact magnetic flows on surfaces, in preparation.
Ginzburg V. L. New generalizations of Poincaré's geometric theorem. Funct. Anal. Appl., 1987, 21(2), 100–106.
Ginzburg V. L. On closed trajectories of a charge in a magnetic field. An application of symplectic geometry. In: Contact and Symplectic Geometry (Cambridge, 1994). Editor: C. B. Thomas. Cambridge: Cambridge University Press, 1996, 131–148. (Publ. Newton Inst., 8.)
Ginzburg V. L. On the existence and non-existence of closed trajectories for some Hamiltonian flows. Math. Z., 1996, 223(3), 397–409.
Ginzburg V. L., Kerman E. Periodic orbits in magnetic fields in dimensions greater than two. In: Geometry and Topology in Dynamics (Winston-Salem, NC, 1998; San Antonio, TX, 1999). Editors: M. Barge and K. Kuperberg. Providence, RI: Amer. Math. Soc., 1999, 113–121. (Contemp. Math., 246.)
Ginzburg V. L., Kerman E. Periodic orbits of Hamiltonian flows near symplectic extrema. Pacific J. Math., 2002, 206(1), 69–91. [Internet: http://www.arXiv.org/abs/math.DG/0011011]
Grinevich P. G., Novikov S. P. Nonselfintersecting magnetic orbits on the plane. Proof of the overthrowing of cycles principle. In: Topics in Topology and Mathematical Physics. Editor: S. P. Novikov. Providence, RI: Amer. Math. Soc., 1995, 59–82. (AMS Transl., Ser. 2, 170.)
Hedlund G. A. Geodesics on a two-dimensional Riemannian manifold with periodic coefficients. Ann. Math., Ser. 2, 1932, 33, 719–739.
Hofer H., Viterbo C. The Weinstein conjecture in cotangent bundles and related results. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 1988, 15(3), 411–445.
Hofer H., Zehnder E. Symplectic Invariants and Hamiltonian Dynamics. Basel: Birkhäuser, 1994. (Birkhäuser Adv. Texts.)
Jiang M.-Y. Hofer-Zehnder symplectic capacity for 2-dimensional manifolds. Proc. Roy. Soc. Edinburgh, Sect. A, 1993, 123(5), 945–950.
Jiang M.-Y. Periodic solutions of Hamiltonian systems on hypersurfaces in a torus. Manuscr. Math., 1994, 85(3–4), 307–321.
Kerman E. Periodic orbits of Hamiltonian flows near symplectic critical submanifolds. Internat. Math. Res. Notices, 1999, 17, 953–969.
Kozlov V. V. Variational calculus in the large and classical mechanics. Russian Math. Surveys, 1985, 40(2), 37–71.
Kozlov V. V. Closed orbits and the chaotic dynamics of a charge in a periodic electromagnetic field. Reg. Khaot. Dinamika, 1997, 2(1), 3–12 (in Russian).
Littlejohn R. G. A guiding center Hamiltonian: a new approach. J. Math. Phys., 1979, 20(12), 2445–2458.
Lu G. The Weinstein conjecture on some symplectic manifolds containing the holomorphic spheres. Kyushu J. Math., 1998, 52(2), 331–351.
Ma R. A remark on Hofer-Zehnder symplectic capacity in symplectic manifolds M × \(\mathbb{R}^{2n} \). Chinese Ann. Math., Ser. B, 1997, 18(1), 89–98.
Macarini L. Entropy rigidity and harmonic fields. Nonlinearity, 2000, 13(5), 1761–1774.
Macarini L. Periodic orbits for Hamiltonian flows and magnetic fields. Preprint, IMPA, 2001.
Mañe R. Lagrangian flows: the dynamics of globally minimizing orbits. In: International Conference on Dynamical Systems (Montevideo, 1995). A tribute to Ricardo Mañé. Editors: F. Ledrappier, J. Lewowicz and S. Newhouse. Harlow: Longman, 1996, 120–131. (Pitman Res. Notes Math. Ser., 362.)
Moser J. Periodic orbits near an equilibrium and a theorem by Alan Weinstein. Commun. Pure Appl. Math., 1976, 29, 727–747.
Nabokov V. Selected letters, 1940–1977. Editors: D. Nabokov and M. J. Bruccoli. San Diego, CA: Harcourt Brace Jovanovich, 1989.
Niche C. On the topological entropy of an optical Hamiltonian flow. Nonlinearity, 2001, 14, 817–827.
Niche C. On the topological entropy of an optical Hamiltonian flow. [Internet: http://www.arXiv.org/abs/math.DS/0010058]
Novikov S. P. The Hamiltonian formalism and a many-valued analogue of Morse theory. Russian Math. Surveys, 1982, 37(5), 1–56.
Novikov S. P., TaĬmanov I. A. Periodic extremals of many-valued or not everywhere positive functionals. Sov. Math. Dokl., 1984, 29(1), 18–20.
Paternain G. P., Paternain M. Anosov geodesic flows and twisted symplectic structures. In: International Conference on Dynamical Systems (Montevideo, 1995). A tribute to Ricardo Mañé. Editors: F. Ledrappier, J. Lewowicz and S. Newhouse. Harlow: Longman, 1996, 132–145. (Pitman Res. Notes Math. Ser., 362.)
Paternain G. P., Paternain M. First derivative of topological entropy for Anosov geodesic flows in the presence of magnetic fields. Nonlinearity, 1997, 10(1), 121–131.
Paternain G. P., Paternain M. Critical values of autonomous Lagrangian systems. Comment. Math. Helvetici, 1997, 72(3), 481–499.
Polterovich L. Geometry on the group of Hamiltonian diffeomorphisms. In: Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998). Doc. Math., 1998, Extra Vol. II, 401–410 (electronic).
TaĬmanov I. A. Closed extremals on two-dimensional manifolds. Russian Math. Surveys, 1992, 47(2), 163–211; errata: 47(4), 247.
TaĬmanov I. A. Closed non-self-intersecting extremals of multivalued functionals. Sib. Math. J., 1992, 33(4), 686–692.
Truc F. Trajectoires bornées d'une particule soumise à un champ magnétique symétrique linéaire. Ann. Institut Henri Poincaré, Physique théorique, 1996, 64(2), 127–154.
Viterbo C. A proof of Weinstein's conjecture in \(\mathbb{R}^{2n} \). Ann. Institut Henri Poincaré, Analyse non linéaire, 1987, 4(4), 337–356.
Weinstein A. Normal modes for nonlinear Hamiltonian systems. Invent. Math., 1973, 20, 47–57.
1981-10 — S. L. Tabachnikov
Chekanov Yu. V. Caustics in geometrical optics. Funct. Anal. Appl., 1986, 20(3), 223–226.
1981-11 — S. V. Chmutov
Arnold V. I. Singularities of Caustics and Wave Fronts. Dordrecht: Kluwer Acad. Publ., 1990. (Math. Appl., Sov. Ser., 62.)
Givental A. B. Singular Lagrangian manifolds and their Lagrangian maps. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics. Newest Results, Vol. 33. Moscow: VINITI, 1988, 55–112 (in Russian) [The English translation: J. Sov. Math., 1990, 52(4), 3246–3278.]
Shcherbak O. P. Wave fronts and reflection groups. Russian Math. Surveys, 1988, 43(3), 149–194.
1981-14 — I. A. Bogaevsky
Arnold V. I. Catastrophe Theory. Berlin: Springer, 1992. [The Russian original 1990.]
Arnold V. I. Mathematical problems in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math. Sci., 100.) [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.]
Roytvarf A. A. The motion of a continuous medium in the force field with a rooted singularity. Moscow Univ. Mech. Bull., 1987, 42(1), 24–27.
Roytvarf A. A. Two-valued velocity field with a square root singularity. Moscow Univ. Mech. Bull., 1988, 43(3), 16–19.
Roytvarf A. A. On the dynamics of a one-dimensional self-gravitating medium. Physica D, 1994, 73(3), 189–204.
1981-16 — S. Yu. Yakovenko
Ecalle J. Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac. Paris: Hermann, 1992. (Actualités Math.)
Il'yashenko Yu. S. Limit cycles of polynomial vector fields with nondegenerate singular points on the real plane. Funct. Anal. Appl., 1984, 18(3), 199–209.
Il'yashenko Yu. S. Dulac's memoir “On limit cycles” and related questions of the local theory of differential equations. Russian Math. Surveys, 1985, 40(6), 1–49.
Il'yashenko Yu. S. Separatrix lunes of analytic vector fields on the plane. Moscow Univ. Math. Bull., 1986, 41(4), 28–35.
Il'yashenko Yu. S. Finiteness theorems for limit cycles. Russian Math. Surveys, 1990, 45(2), 129–203.
Il'yashenko Yu. S. Finiteness Theorems for Limit Cycles. Providence, RI: Amer. Math. Soc., 1991. (Transl. Math. Monographs, 94.)
1981-18 — B. A. Khesin
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
Katok A. B. Lyapunov exponents, entropy and periodic points for diffeomorphisms. Inst. Hautes Études Sci. Publ. Math., 1980, 51, 137–174.
Klapper I., Young L.-S. Rigorous bounds on the fast dynamo growth rate involving topological entropy. Commun. Math. Phys., 1995, 173(3), 623–646.
KozlovskiĬ O. S. An integral formula for topological entropy of C∞ maps. Ergod. Theory Dynam. Systems, 1998, 18(2), 405–424.
KozlovskiĬ O. S. Private communication, 2000; paper in preparation.
Lattès S. Sur l'itération des substitutions rationnelles et les fonctions de Poincaré. C. R. Acad. Sci. Paris, 1918, 166(1), 26–28; erratum: 1918, 166(2), 88.
Lyubich M. Dynamics of rational transformations: topological picture. Russian Math. Surveys, 1986, 41(4), 43–117.
1981-21 — A. A. Davydov
Davydov A. A. Structural stability of control systems on orientable surfaces. Math. USSR, Sb., 1992, 72(1), 1–28.
1981-22 — V. P. Rostov, S. K. Lando
Arnold V. I. Classification of the Poisson structures on the plane. Uspekhi Mat. Nauk, 1984, 39(5), 256 (in Russian).
Arnold V. I. Remarks on Poisson structures on the plane and other powers of volume forms. Trudy Semin. Petrovskogo, 1987, 12, 37–46 (in Russian) [The English translation: J. Sov. Math., 1989, 47(3), 2509–2516.]
Givental A. B. Lagrangian manifolds with singularities and irreducible sl2-modules. Russian Math. Surveys, 1983, 38(6), 121–122.
Kostov V. P. Versal deformations of differential forms of degree α on the line. Funct. Anal. Appl., 1984, 18(4), 335–337.
Kostov V. P. Versal deformations of differential forms of real power on a line. Math. USSR, Izv., 1991, 37(3), 525–537.
Kostov V. P., Lando S. K. Versal deformations of powers of volume forms. In: Computational Algebraic Geometry (Nice, 1992). Editors: F. Eyssette and A. Galligo. Boston, MA: Birkhäuser, 1993, 143–162. (Progr. Math., 109.)
Lando S. K. Deformations of differential forms. Ph. D. Thesis, Moscow State University, 1985 (in Russian).
Lando S. K. Normal forms of the degrees of a volume form. Funct. Anal. Appl., 1985, 19(2), 146–148.
Lando S. K. Deformations of differential forms. Proc. Steklov Inst. Math., 1995, 209, 145–173.
Varchenko A. N. Local classification of volume forms in the presence of a hypersurface. Funct. Anal. Appl., 1985, 19(4), 269–276.
1981-23 — V. A. Vassiliev
Kulikov V. S. Calculation of singularities of an imbedding of a generic algebraic surface in projective space P3. Funct. Anal. Appl., 1983, 17(3), 176–186.
Salmon G. Treatise on the Analytic Geometry of Three Dimensions, Vol. II, 5th edition. London: Longmans and Green, 1914; reprinted by Chelsea: New York, 1965.
1981-24 — S. V. Chmutov
Arnold V. I., Gusein-Zade S. M., Varchenko A. N. Singularities of Differentiable Maps, Vol. II: Monodromy and Asymptotics of Integrals. Boston, MA: Birkhäuser, 1988. (Monographs in Math., 83.) [The Russian original 1984.]
Barth W. Two projective surfaces with many nodes, admitting the symmetries of the icosahedron. J. Algebraic Geom., 1996, 5(1), 173–186.
Beauville A. Sur le nombre maximum de points doubles d'une surface dans P3 (µ(5) =31). J. Géométrie Algébrique d'Angers/Algebraic Geometry (Angers, 1979). Editor: A. Beauville. Sijthoff and Noordhoff, 1980, 207–215.
Bruce J. W. An upper bound for the number of singularities on a projective hypersurface. Bull. London Math. Soc., 1981, 13(1), 47–50.
Burkhardt H. Untersuchungen aus dem Gebiete der hyperelliptischen Modulfunktionen, Zweiter Teil. Math. Ann., 1891, 38, 161–224.
Chmutov S. V. Examples of projective surfaces with many singularities. J. Algebraic Geom., 1992, 1(2), 191–196.
Givental A. B. Maximum number of singular points on a projective hypersurface. Funct. Anal. Appl., 1983, 17(3), 223–225.
Goryunov V. V. Symmetric quartics with many nodes. In: Singularities and Bifurcations. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1994, 147–161. (Adv. Sov. Math., 21.)
Jaffe D. B., Ruberman D. A sextic surface cannot have 66 nodes. J. Algebraic Geom., 1997, 6(1), 151–168.
Kalker T. Cubic fourfolds with fifteen ordinary double points. Ph.D. Thesis, Leiden, 1986.
Miyaoka Y. The maximal number of quotient singularities on surfaces with given numerical invariants. Math. Ann., 1984, 268(2), 159–171.
Togliatti E. G. Sulle superficie algebriche col massimo numero di punti doppi. Rend. Semin. Mat. Univ. Politec. Torino, 1950, 9, 47–59.
1981-26 — D. A. Popov
Colin de Verdière Y. Nombre de points entiers dans une famille homothétique de domaines de \(\mathbb{R}^n \). Ann. Sci. École Norm. Sup., Sér. 4, 1977, 10(4), 559–575.
Huxley M. N. Exponential sums and lattice points, II. Proc. London Math. Soc., Ser. 3, 1993, 66(2), 279–301.
Kosygin D. V., Minasov A. A., SinaĬ Ya. G. Statistical properties of the spectra of Laplace-Beltrami operators on Liouville surfaces. Russian Math. Surveys, 1993, 48(4), 1–142.
Loo-Keng Hua. Abschätzungen von Exponentialsummen und ihre Anwendung in der Zahlentheorie. Leipzig: B. G. Teubner, 1959.
MÜLLER W., NOWAK W. G. Lattice points in planar domains: applications of Huxley's “discrete Hardy-Littlewood method.” In: Number-Theoretic Analysis (Vienna, 1988–1989). Editors: H. Hlawka and R. F. Tichy. Berlin: Springer, 1990, 139–164. (Lecture Notes in Math., 1452.)
Popov D. A. On the number of lattice points in three-dimensional bodies of revolution. Izv. Math., 2000, 64(2), 343–361.
Randol B. On the Fourier transform of the indicator function of a planar set. Trans. Amer. Math. Soc., 1969, 139, 271–278.
Randol B. On the asymptotic behavior of the Fourier transform of the indicator function of a convex set. Trans. Amer. Math. Soc., 1969, 139, 279–285.
Varchenko A. N. On the number of integer points in families of homothetic domains in \(\mathbb{R}^n \). Funct. Anal. Appl., 1983, 17(2), 79–83.
Vinogradov I. M. Special Variants of the Method of Trigonometric Sums. Moscow: Nauka, 1976 (in Russian).
1981-26 — M. B. Sevryuk
Arnold V. I., Gusein-Zade S. M., Varchenko A. N. Singularities of Differentiable Maps, Vol. II: Monodromy and Asymptotics of Integrals. Boston, MA: Birkhäuser, 1988, §6, n°6.7. (Monographs in Math., 83.) [The Russian original 1984.]
Batyrev V. V., Manin Yu. I. Sur le nombre des points rationnels de hauteur borné des variétés algèbriques. Math. Ann., 1990, 286(1–3), 27–43. [Reprinted in: Selected Papers of Yu. I. Manin. River Edge, NJ: World Scientific, 1996, 373–389.]
Colin de Verdière Y. Nombre de points entiers dans une famille homothétique de domaines de \(\mathbb{R}^n \). Ann. Sci. École Norm. Sup., Sér. 4, 1977, 10(4), 559–575.
Popov D. A. Estimates with constants for some classes of oscillating integrals. Russian Math. Surveys, 1997, 52(1), 73–145.
Randol B. A lattice-point problem. I; II. Trans. Amer. Math. Soc., 1966, 121, 257–268; 125, 101–113.
Randol B. On the Fourier transform of the indicator function of a planar set. Trans. Amer. Math. Soc., 1969, 139, 271–278.
Randol B. On the asymptotic behavior of the Fourier transform of the indicator function of a convex set. Trans. Amer. Math. Soc., 1969, 139, 279–285.
Varchenko A. N. On the number of integer points in a domain. Russian Math. Surveys, 1982, 37(3), 223–224.
Varchenko A. N. On the number of integer points in families of homothetic domains in \(\mathbb{R}^n \). Funct. Anal. Appl., 1983, 17(2), 79–83.
1981-28 — I. A. Bogaevsky
Bogaevsky I. A. Singularities of convex hulls of three-dimensional hypersurfaces. Proc. Steklov Inst. Math., 1998, 221, 71–90.
Sedykh V. D. Functional moduli of singularities of convex hulls of manifolds of codimension 1 and 2. Math. USSR, Sb., 1984, 47, 223–236.
Sedykh V. D. Stabilization of singularities of convex hulls. Math. USSR, Sb., 1989, 63(2), 499–505.
Sedykh V. D. The sewing of a swallowtail and a Whitney umbrella in a four-dimensional controlled system. In: Proceedings of Gubkin State Oil and Gas Academy. Moscow: Neft’ i Gaz, 1997, 58–68 (in Russian).
Zakalyukin V. M. Singularities of convex hulls of smooth manifolds. Funct. Anal. Appl., 1977, 11(3), 225–227.
1982-2 — B. A. Khesin
Vaintrob A. Yu. Darboux theorem and equivariant Morse lemma. J. Geom. Phys., 1996, 18(1), 59–75.
1982-5 — M. B. Sevryuk
Arnold V. I. Remarks on the perturbation theory for Mathieu type problems. Russian Math. Surveys, 1983, 38(4), 215–233.
Galkin O. G. Resonance regions for Mathieu type dynamical systems. Russian Math. Surveys, 1989, 44(3), 191–192.
Galkin O. G. Resonance regions for Mathieu type dynamical systems on a torus. Physica D, 1989, 39(2–3), 287–298.
Galkin O. G. Phase-locking for Mathieu type vector fields on the torus. Funct. Anal. Appl., 1992, 26(1), 1–6.
Galkin O. G. Phase-locking for maps of a torus: a computer assisted study. Chaos, 1993, 3(1), 73–82.
Galkin O. G. Phase-locking for Mathieu type mappings of the torus. Funct. Anal. Appl., 1993, 27(1), 1–9.
Galkin O. G. Phase-locking for dynamical systems on the torus and perturbation theory for Mathieu-type problems. J. Nonlinear Sci., 1994, 4(2), 127–156.
1982-6 — B. A. Khesin
Arnold V. I. Some remarks on the antidynamo theorem. Moscow Univ. Math. Bull., 1982, 37(6), 57–66.
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
1982-7 — B. Z. Shapiro
Matov V. I. Elliptic domains of general families of homogeneous polynomials and extreme functions. Funct. Anal. Appl., 1985, 19(2), 102–111.
Vainshtein A. D., Shapiro B. Z. Singularities of hyperbolic polynomials and of the boundary of the hyperbolicity domain. Uspekhi Mat. Nauk, 1985, 40(6), 305 (in Russian)
Vainshtein A. D., Shapiro B. Z. Singularities of the boundary of the hyperbolicity domain. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics. Newest Results, Vol. 33. Moscow: VINITI, 1988, 193–214 (in Russian). [The English translation: J. Sov. Math., 1990, 52(4), 3326–3337.]
1982-7 — V. A. Vassiliev
Arnold V. I., Vassiliev V. A., Goryunov V. V., Lyashko O. V. Singularity Theory. II. Classification and Applications. Berlin: Springer, 1993. (Encyclopædia Math. Sci., 39; Dynamical Systems, VIII.) [The Russian original 1989.]
Matov V. I. The topological classification of germs of the maximum and minimax functions of a family of functions in general position. Russian Math. Surveys, 1982, 37(4), 127–128.
Matov V. I. Elliptic domains of general families of homogeneous polynomials and extreme functions. Funct. Anal. Appl., 1985, 19(2), 102–111.
Matov V. I. Extremum functions of finite families of convex homogeneous functions. Funct. Anal. Appl., 1987, 21(1), 42–52.
1982-16 — S. K. Lando
Steenbrink J. Semicontinuity of the singularity spectrum. Invent. Math., 1985, 79(3), 557–565.
Varchenko A. N. Asymptotic integrals and Hodge structures. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics, Vol. 22. Moscow: VINITI, 1983, 130–166 (in Russian). [The English translation: J. Sov. Math., 1984, 27, 2760–2784.]
1982-17
Vainshtein A. D., Shapiro B. Z. Higher-dimensional analogs of the theorems of Newton and Ivory. Funct. Anal. Appl., 1985, 19(1), 17–20.
1983-1 — Yu. M. Baryshnikov, M. Garay
Arnold V. I. Vanishing inflections. Funct. Anal. Appl., 1984, 18(2), 128–130.
Baryshnikov Y. Real vanishing inflections and boundary singularities. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 129–136. (Adv. Sov. Math., 1.)
Plücker J. System Der Analytischen Geometrie (1834). In: Gesammelte Wissenschatfliche Abhandlungen, Band 1, Vol. 2. Leipzig: B. G. Teubner, 1898.
Salmon G. A Treatise on the Analytic Geometry of Three Dimensions. Dublin: Hodges, Smith & Co., 1865. [The German extended translation: Salmon G., Fiedler R. Analytische Geometrie des Raumes, II Teil. Leipzig: B. G. Teubner, 1880.]
1983-3 — M. B. Sevryuk
Arnold V. I. Sur une propriété topologique des applications globalement canoniques de la mécanique classique. C. R. Acad. Sci. Paris, 1965, 261(19), 3719–3722. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 81–86.]
Arnold V. I. The stability problem and ergodic properties of classical dynamical systems. In: Proceedings of the International Congress of Mathematicians (Moscow, 1966). Moscow: Mir, 1968, 387–392 (in Russian). [The English translation: AMS Transl., Ser. 2, 1968, 70, 5–11.] [The original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 95–101.]
Arnold V. I. A comment to H. Poincaré's paper “Sur un théorème de géométrie.” In: Poincaré H. Selected Works in Three Volumes (in Russian). Editors: N. N. Bogolyubov, V. I. Arnold and I. B. Pogrebysskiĭ. Vol. II. New methods of celestial mechanics. Topology. Number theory. Moscow: Nauka, 1972, 987–989 (in Russian).
Arnold V. I. Fixed points of symplectic diffeomorphisms. In: Problems of present day mathematics. Editor: F. E. Browder. In: Mathematical Developments Arising from Hilbert Problems (Northern Illinois University, 1974). Part 1. Editor: F. E. Browder. Providence, RI: Amer. Math. Soc., 1976, 35–79; see XX, p. 66. (Proc. Symposia Pure Math., 28.)
Arnold V. I. Some problems in the theory of differential equations. In: Unsolved Problems of Mechanics and Applied Mathematics. Moscow: Moscow University Press, 1977, 3–9 (in Russian).
Arnold V. I. Reversible systems. In: Nonlinear and Turbulent Processes in Physics (Kiev, 1983), V.3. Editor: R. Z. Sagdeev. Chur: Harwood Acad. Publ., 1984, 1161–1174. [For the Russian translation see, e. g.: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 355–363.]
Arnold V. I. Mathematical Methods of Classical Mechanics, 2nd edition. New York: Springer, 1989, Appendix 9. (Graduate Texts in Math., 60.) [The Russian original 1974.]
Bredon G. E. Introduction to Compact Transformation Groups. New York: Academic Press, 1972.
Conley C. C., Zehnder E. The Birkhoff-Lewis fixed point theorem and a conjecture of V. I. Arnold. Invent. Math., 1983, 73(1), 33–49.
Conner P. E. Differentiable Periodic Maps. Berlin: Springer, 1979. (Lecture Notes in Math., 738.)
Conner P. E., Floyd E. E. Differentiable Periodic Maps. Berlin: Springer, 1964.
Lamb J. S. W. Reversing symmetries in dynamical systems. Ph. D. Thesis, University of Amsterdam, 1994.
Lamb J. S. W., Roberts J. A. G. Time-reversal symmetry in dynamical systems: a survey. Physica D, 1998, 112(1–2), 1–39.
Montaldi J. Caustics in time reversible Hamiltonian systems. In: Singularity Theory and its Applications, Part II. Editors: M. Roberts and I. Stewart. Berlin: Springer, 1991, 266–277. (Lecture Notes in Math., 1463.)
Roberts J. A. G. Some characterisations of low-dimensional dynamical systems with time-reversal symmetry. In: Control and Chaos. Editors: K. Judd, A. Mees, K. L. Teo and T. L. Vincent. Boston, MA: Birkhäuser, 1997, 106–133. (Math. Model., 8.)
Roberts J. A. G., Quispel G. R. W. Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems. Phys. Rep., 1992, 216(2–3), 63–177.
Sevryuk M. B. Reversible Systems. Berlin: Springer, 1986. (Lecture Notes in Math., 1211.)
Sevryuk M. B. Lower-dimensional tori in reversible systems. Chaos, 1991, 1(2), 160–167.
1983-4 — S. L. Tabachnikov
Chekanov Yu. V. Asymptotic behavior of the number of maxima of the product of linear functions of two variables. Vestnik Moskov. Univ. Ser. Mat. Mekh., 1986, № 3, 93–94 (in Russian).
1983-5 — S. V. Chmutov
Durfee A., Kronenfeld N., Munson H., Roy J., Westby I. Counting critical points of real polynomials in two variables. Amer. Math. Monthly, 1993, 100(3), 255–271.
Durfee A. The index of grad f(x,y). Topology, 1998, 37(6), 1339–1361.
Shustin E. Critical points of real polynomials, subdivisions of Newton polyhedra and topology of real algebraic hypersurfaces. In: Topology of Real Algebraic Varieties and Related Topics. Dedicated to the memory of Dmitriĭ Andreevich Gudkov. Editors: V. Kharlamov, A. Korchagin, G. Polotovskiĭ and O. Viro. Providence, RI: Amer. Math. Soc., 1996, 203–223. (AMS Transl., Ser. 2, 173; Adv. Math. Sci., 29.)
1983-7 — A. A. Glutsyuk
Herman M. R. Majoration du nombre de cycles périodiques pour certaines familles de difféomorphismes du cercle. An. Acad. Brasil. Ciênc., 1985, 57(3), 261–263.
Yakobson M. V. On the number of periodic trajectories for analytic diffeomorphisms of the circle. Funct. Anal. Appl., 1985, 19(1), 79–80.
1983-14 — B. A. Khesin
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
1984-1 — B. Z. Shapiro
Shapiro B. Z. Linear differential equations and real flag manifolds. Funct. Anal. Appl., 1989, 23(1), 82–83.
Shapiro B. Z. Space of linear differential equations, and flag manifolds. Math. USSR, Izv., 1991, 36(1), 183–197.
1984-6 — B. S. Kruglikov
Arnold V. I. Small denominators and problems of stability of motion in classical and celestial mechanics. Russian Math. Surveys, 1963, 18(6), 85–191.
Arnold V. I. Mathematical Methods of Classical Mechanics, 2nd edition. New York: Springer, 1989. (Graduate Texts in Math., 60.) [The Russian original 1974.]
Conn J. F. Linearization of analytic Poisson structures. Ann. Math., Ser. 2, 1984, 119(3), 577–601.
Conn J. F. Normal forms for smooth Poisson structures. Ann. Math., Ser. 2, 1985, 121(3), 565–593.
Dufour J.-P. Linéarisation de certaines structures de Poisson. J. Differ. Geom., 1990, 32(2), 415–428.
Dufour J.-P. Une nouvelle famille d'algèbres de Lie non dégénérées. Indag. Math. (N. S.), 1995, 6(1), 67–82.
Lychagin V. V. Spectral sequences and normal forms of Lie algebras of vector fields. Russian Math. Surveys, 1983, 37(5), 152–153.
Lychagina O. V. Normal forms of Poisson structures. Math. Notes, 1997, 61(2), 180–192.
Lychagina O. V. Degenerate Poisson structures in dimension 3. Math. Notes, 1998, 63(4), 509–521.
Wade A. Normalisation formelle de structures de Poisson. C. R. Acad. Sci. Paris, Sér. I Math., 1997, 324(5), 531–536.
Weinstein A. The local structure of Poisson manifolds. J. Differ. Geom., 1983, 18(3), 523–557.
1984-7 — A. A. Bolibruch
Bolibruch A. A. Regular singular points as isomonodromic confluences of Fuchsian singularities. Russian Math. Surveys, 2001, 56(4), 745–746.
Glutsyuk A. Stokes operators via limit monodromy of generic perturbation. J. Dynam. Control Systems, 1999, 5(1), 101–135.
Kostov V. P. Normal forms for systems of linear differential equations with bifurcating Fuchsian singularities. Differ. Uravneniya, 1990, 26(2), 353–356 (in Russian, for the English translation see Differ. Equations).
Ramis J.-P. Phénomène de Stokes et resommation. C. R. Acad. Sci. Paris, Sér. I Math., 1985, 301(4), 99–102.
1984-7 — A. A. Glutsyuk, V. P. Kostov
Balser W., Jurkat W. B., Lutz D. A. Birkhoff invariants and Stokes’ multipliers for meromorphic linear differential equations. J. Math. Anal. Appl., 1979, 71(1), 48–94.
Bolibruch A. A. On isomonodromic deformations of Fuchsian systems. J. Dynam. Control Systems, 1997, 3(4), 589–604.
Bolibruch A. A. On isomonodromic confluences of Fuchsian singularities. Proc. Steklov Inst. Math., 1998, 221, 117–132.
Duval A. Biconfluence et groupe de Galois. J. Fac. Sci. Tokyo, Sect. IA Math., 1991, 38(2), 211–223.
Garnier R. Sur les singularités irrégulières des équations différentielles linéaires. J. Math. Pures Appl., Sér. 8, 1919, 2, 99–198.
Glutsyuk A. A. Stokes operators via limit monodromy of generic perturbation. J. Dynam. Control Systems, 1999, 5(1), 101–135.
Glutsyuk A. A. Confluence of singular points and the nonlinear Stokes phenomena. Trudy Moskov. Mat. Obshch., 2000, 62, 54–104 (in Russian, for the English translation see Trans. Moscow Math. Soc.).
Jurkat W. B., Lutz D. A., Peyerimhoff A. Birkhoff invariants and effective calculations for meromorphic linear differential equations. J. Math. Anal. Appl., 1976, 53(2), 438–470.
Kostov V. P. Normal forms for systems of linear differential equations with bifurcating Fuchsian singularities. Differ. Uravneniya, 1990, 26(2), 353–356 (in Russian, for the English translation see Differ. Equations).
Kostov V. P. Miniversal and isomonodromic deformations of Fuchsian systems with bifurcation poles. Differ. Equations, 1990, 26(5), 561–571.
Kostov V. P. Normal forms of unfoldings of non-Fuchsian systems. In: Aspects of Complex Analysis, Differential Geometry, Mathematical Physics and Applications (St. Konstantin, 1998). Editors: S. Dimiev and K. Sekigawa. River Edge, NJ: World Scientific, 1999, 1–18. [Prépublication Université de Nice, no. 348, juin 1993.]
Kostov V. P. Normal forms of unfoldings of non-Fuchsian systems. C. R. Acad. Sci. Paris, Sér. I Math., 1994, 318(7), 623–628.
Martinet J. Remarques sur la bifurcation nœud-col dans le domaine complexe. In: Singularités d'équations différentielles (Dijon, 1985). Astérisque, 1987, 150–151, 131–149.
Ramis J.-P. Confluence et résurgence. J. Fac. Sci. Tokyo, Sect. IA Math., 1989, 36(3), 703–716.
Sibuya Y. Stokes phenomena. Bull. Amer. Math. Soc., 1977, 83(5), 1075–1077.
Zhang C. Quelques études en théorie des équations fonctionnelles et en analyse combinatoire. Thèse, Institut de Recherche Mathematique Avancée, Université Louis Pasteur et CNRS (URA 01), 1994.
1984-8 — S. V. Chmutov
Chmutov S. V. Monodromy groups of critical points of functions, I; II. Invent. Math., 1982, 67(1), 123–131; 1983, 73(3), 491–510.
Janssen W. A. M. Skew-symmetric vanishing lattices and their monodromy groups, I; II. Math. Ann., 1983, 266(1), 115–133; 1985, 272(1), 17–22.
Shapiro B., Shapiro M., Vainshtein A. Connected components in the intersection of two open opposite Schubert cells in SLn\({\text{(}}\mathbb{R}{\text{)}}/B\). Internat. Math. Res. Notices, 1997, 10, 469–493.
Shapiro B., Shapiro M., Vainshtein A. Skew-symmetric vanishing lattices and intersections of Schubert cells. Internat. Math. Res. Notices, 1998, 11, 563–588.
Shapiro B., Shapiro M., Vainshtein A., Zelevinsky A. Simply laced Coxeter groups and groups generated by symplectic transvections. Michigan Math. J., 2000, 48, 531–551.
Wajnryb B. On the monodromy group of plane curve singularities. Math. Ann., 1979/80, 246(2), 141–154.
1984-10 — S. Yu. Yakovenko
Arnold V. I. The Sturm theorems and symplectic geometry. Funct. Anal. Appl., 1985, 19(4), 251–259.
Arnold V. I. Sur quelques problèmes de la théorie des systèmes dynamiques. Topol. Methods Nonlinear Anal., 1994, 4(2), 209–225. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 533–551.]
Givental A. B. Sturm's theorem for hyperelliptic integrals. Leningrad Math. J., 1990, 1(5), 1157–1163.
Novikov D. I., Yakovenko S. Yu. Redundant Picard-Fuchs system for Abelian integrals. J. Differ. Equations, 2001, 177(2), 267–306.
1984-12 — B. A. Khesin
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
Garnett L. Foliations, the ergodic theorem and Brownian motion. J. Funct. Anal., 1983, 51(3), 285–311.
Khesin B. A. Ergodic interpretation of integral hydrodynamic invariants. J. Geom. Phys., 1992, 9(1), 101–110.
Riviére T. High-dimensional helicities and rigidity of linked foliations. Preprint, Courant Institute, New York, 1999.
1984-16 — M. B. Sevryuk
KozlovskiĬ O. S. Resonance zone boundaries for families of circle diffeomorphisms. Physica D, 1991, 54(1–2), 1–4.
1984-22 — B. A. Khesin
Carneiro M. J. D., Palis J. Bifurcations and global stability of families of gradients. Inst. Hautes Études Sci. Publ. Math., 1989, 70, 103–168.
Khesin B. A. Bifurcations of gradient dynamical systems. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics. Newest Results, Vol. 33. Moscow: VINITI, 1988, 113–155, 236 (in Russian). [The English translation: J. Sov. Math., 1990, 52(4), 3279–3305.]
Vegter G. Bifurcations of gradient vectorfields. In: Bifurcations, Theorie Ergodique et Applications (Dijon, 1981). Astérisque, 1982, 98–99, 39–73.
Vegter G. Bifurcations of gradient vector fields. Ph.D. Thesis, University of Groningen, 1983.
1985-5 — E. Ferrand
Mohnke K. Holomorphic disks and the chord conjecture. [Internet: http://xxx.arXiv.org/abs/math.SG/0008014]
1985-7 — V. A. Vassiliev
Arnold V. I. On some topological invariants of algebraic functions. Trans. Moscow Math. Soc., 1970, 21, 30–52.
Arnold V. I. Spaces of functions with moderate singularities. Funct. Anal. Appl., 1989, 23(3), 169–177. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 455–469].
Nekrasov N. A. On the cohomology of the complement of the bifurcation diagram of the singularity Aμ. Funct. Anal. Appl., 1993, 27(4), 245–250.
Vassiliev V. A. Stable cohomologies of the complements of the discriminants of deformations of singularities of smooth functions. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics. Newest Results, Vol. 33. Moscow: VINITI, 1988, 3–29 (in Russian). [The English translation: J. Sov. Math., 1990, 52(4), 3217–3230.]
Vassiliev V. A. Topology of complements to discriminants and loop spaces. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 9–21. (Adv. Sov. Math., 1.)
Vassiliev V. A. Topology of Complements to Discriminants. Moscow: PHASIS, 1997 (in Russian).
1985-8 — Yu. M. Baryshnikov, M. Garay
Arnold V. I. Wave front evolution and equivariant Morse lemma. Commun. Pure Appl. Math., 1976, 29(6), 557–582; correction: 1977, 30(6), 823. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 289–318.]
Bruce J. W., Giblin P. J., Tari F. Families of surfaces: height functions and projections to planes. Math. Scand., 1998, 82(2), 165–185.
Garay M. The classical and Legendrian theory of vanishing flattening points of plane and spatial curves. Ph.D. Thesis, Université Paris 7, 2001.
Kazarian M. E. Singularities of the boundary of fundamental systems, flattenings of projective curves, and Schubert cells. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics. Newest Results, Vol. 33. Moscow: VINITI, 1988, 215–234 (in Russian). [The English translation: J. Sov. Math., 1990, 52, 3338–3349.]
Kazarian M. E. Bifurcations of flattenings and Schubert cells. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 145–156. (Adv. Sov. Math., 1.)
Kazarian M. E. Flattening of projective curves, singularities of Schubert stratifications of Grassmannians and flag varieties, and bifurcations of Weierstrass points of algebraic curves. Russian Math. Surveys, 1991, 46(5), 91–136.
1985-13 — M. L. Kontsevich
Fulton W. Eigenvalues, invariant factors, highest weights, and Schubert calculus. [Internet: http:/www.arXiv.org/abs/math.AG/9908012]
Roberts J. Classical 6j-symbols and the tetrahedron. Geometry & Topology, 1999, 3, 21–66 (electronic). [Internet: http:/www.arXiv.org/abs/math-ph/9812013]
1985-14 — V. N. Karpushkin
Karpushkin V. N. Uniform estimates of volumes. Proc. Steklov Inst. Math., 1998, 221, 214–220.
Varchenko A. N. Newton polyhedra and estimation of oscillating integrals. Funct. Anal. Appl., 1976, 10(3), 175–196.
Vassiliev V. A. The asymptotic of exponential integrals, Newton diagrams, and classification of minimum points. Funct. Anal. Appl., 1977, 11(3), 163–172.
1985-15 — V. I. Arnold
Givental A. B. Singular Lagrangian manifolds and their Lagrangian mappings. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics. Newest Results, Vol. 33. Moscow: VINITI, 1988, 55–112 (in Russian). [The English translation: J. Sov. Math., 1990, 52, 3246–3278.]
1985-19 — V. P. Rostov
Arnold V. I. Hyperbolic polynomials and Vandermonde mappings. Funct. Anal. Appl., 1986, 20(2), 52–53.
Givental A. B. Moments of random variables and the equivariant Morse lemma. Russian Math. Surveys, 1987, 42(2), 275–276.
Kostov V. P. On the geometric properties of Vandermonde's mapping and on the problem of moments. Proc. Roy. Soc. Edinburgh, Sect. A, 1989, 112(3–4), 203–211.
Kostov V. P. On the hyperbolicity domain of the polynomial xn + a1xn−1 + … + an, Serdica Math. J., 1999, 25(1), 47–70.
Rostov V. P. Discriminant sets of families of hyperbolic polynomials of degree 4 and 5. Serdica Math. J., 2002, 28(2), 117–152. [Prépublication Université de Nice, no. 620, juin 2001.]
Kostov V. P., Shapiro B. Z. On arrangements of roots for a real hyperbolic polynomial and its derivatives. Bull. Sci. Math., 2002, 126(1), 45–60. [Prépublication Université de Nice, no. 619, juin 2001.]
Meguerditchian I. A theorem on the escape from the space of hyperbolic polynomials. Math. Z., 1992, 211(3), 449–460.
Meguerditchian I. Géométrie du discriminant réel et des polynômes hyperboliques. Thèse de doctorat, Université de Rennes I, soutenue le 24.01.1991.
Meguerditchian I. Géométrie locale des polynômes hyperboliques. C. R. Acad. Sci. Paris, Sér. I Math., 1991, 312(11), 849–852.
Shapiro B. Z., Shapiro M. Z. This strange and mysterious Rolle's theorem. Amer. Math. Monthly, submitted.
1985-20 — B. A. Khesin
Kharlamov V. M. Homotopy of real homogeneous vector fields. Uspekhi Mat. Nauk, 1983, 38(5), 173 (in Russian).
Khesin B. A. Homogeneous vector fields and the Whitney umbrellas. Russian Math. Surveys, 1987, 42(5), 171–172.
1985-22 — F. Napolitano
Arnold V. I. On some topological invariants of algebraic functions. Trans. Moscow Math. Soc., 1970, 21, 30–52.
Arnold V. I. Topological classification of complex trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges. Funct. Anal. Appl., 1996, 30(1), 1–14.
Napolitano F. Discriminant and bifurcation diagram of complex trigonometric polynomials. C. R. Acad. Sci. Paris, Sér. I Math., 1998, 327(8), 771–776.
Napolitano F. Topology of complements of strata of the discriminant of polynomials. C. R. Acad. Sci. Paris, Sér. I Math., 1998, 327(7), 665–670.
Nekrasov N. A. On the cohomology of the complement of the bifurcation diagram of the singularity Aμ. Funct. Anal. Appl., 1993, 27(4), 245–250.
1985-22 — V. A. Vassiliev
Nekrasov N. A. On the cohomology of the complement of the bifurcation diagram of the singularity Aμ. Funct. Anal. Appl., 1993, 27(4), 245–250.
Vassiliev V. A. Stable cohomologies of the complements of the discriminants of deformations of singularities of smooth functions. In: Itogi Nauki i Tekhniki VINITI. Current Problems in Mathematics. Newest Results, Vol. 33. Moscow: VINITI, 1988, 3–29 (in Russian). [The English translation: J. Sov. Math., 1990, 52(4), 3217–3230.]
Vassiliev V. A. Complements of Discriminants of Smooth Maps: Topology and Applications, revised edition. Providence, RI: Amer. Math. Soc., 1994. (Transl. Math. Monographs, 98.)
1986-1 — E. Ferrand
Viterbo C. Properties of embedded Lagrange manifolds. In: First European Congress of Mathematics (Paris, July 6–10, 1992), Vol. II. Invited lectures, Part 2. Editors: A. Joseph, F. Mignot, F. Murat, B. Prum and R. Rentschler. Basel: Birkhäuser, 1994, 463–474. (Progr. Math., 120.)
1986-4 — M. B. Sevryuk
Arnold V. I. Reversible systems. In: Nonlinear and Turbulent Processes in Physics (Kiev, 1983), V.3. Editor: R. Z. Sagdeev. Chur: Harwood Acad. Publ., 1984, 1161–1174. [For the Russian translation see, e. g.: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 355–363.]
Arnold V. I. Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd edition. New York: Springer, 1988. (Grundlehren der Mathematischen Wissenschaften, 250.) [The Russian original 1978.]
Arnold V. I., Kozlov V. V., NeĬshtadt A. I. Mathematical Aspects of Classical and Celestial Mechanics, 2nd edition. Berlin: Springer, 1993. (Encyclopaedia Math. Sci., 3; Dynamical systems, III.) [The Russian original 1985.] [The second, revised and supplemented, Russian edition 2002.]
Arnold V. I., Sevryuk M. B. Oscillations and bifurcations in reversible systems. In: Nonlinear Phenomena in Plasma Physics and Hydrodynamics. Editor: R. Z. Sagdeev. Moscow: Mir, 1986, 31–64.
Bruno A. D. Analytical form of differential equations. I; II. Trans. Moscow Math. Soc., 1971, 25, 131–288; 1972, 26, 199–239.
Cotter C. The 1: 1 semisimple resonance. Ph.D. thesis, University of California at Santa Cruz, 1986.
Cotter C. Bifurcations of Hamiltonian periodic orbits near an equilibrium in 1: 1 resonance. Abstracts of Papers Presented to the AMS, 1987 (issue 53), 8(6), 394–395.
Devaney R. L. Reversible diffeomorphisms and flows. Trans. Amer. Math. Soc., 1976, 218, 89–113.
Duistermaat J. J. Bifurcations of periodic solutions near equilibrium points of Hamiltonian systems. In: Bifurcation Theory and Applications. Editor: L. Salvadori. Berlin: Springer, 1984, 57–105. (Lecture Notes in Math., 1057.)
Henrard J. Periodic orbits emanating from a resonant equilibrium. Celest. Mech., 1970, 1(3/4), 437–466.
Lahiri A., Bhowal A., Roy T. K., Sevryuk M. B. Stability of invariant curves in four-dimensional reversible mappings near 1: 1 resonance. Physica D, 1993, 63(1–2), 99–116.
Lyapunov A. M. An analysis of one of the special cases in the problem of the stability of motion. In: Collected Papers, Vol. II. Moscow-Leningrad: the USSR Academy of Sciences Press, 1956, 272–331 (in Russian). [The original publication 1893.]
Lyapunov A. M. The General Problem of the Stability of Motion. London: Taylor & Francis, 1992. [The Russian original 1892.] [The first French translation 1907.]
Malomed B. A., Tribelsky M. I. Bifurcations in distributed kinetic systems with aperiodic instability. Physica D, 1984, 14(1), 67–87.
van der Meer J.-C. The Hamiltonian Hopf Bifurcation. Berlin: Springer, 1985. (Lecture Notes in Math., 1160.)
van der Meer J.-C. Bifurcation at nonsemisimple 1: −1 resonance. Z. Angew. Math. Phys., 1986, 37(3), 425–437.
Schmidt D. S. Periodic solutions near a resonant equilibrium of a Hamiltonian system. Celest. Mech., 1974, 9(1), 81–103.
Sevryuk M. B. Reversible Systems. Berlin: Springer, 1986. (Lecture Notes in Math., 1211.)
Sevryuk M. B. Reversible dynamical systems. Ph.D. Thesis, Moscow State University, 1987 (in Russian).
1986-6 — B. A. Khesin
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
Eliashberg Ya. M., Ratiu T. On the diameter of the symplectomorphism group of the ball. In: Symplectic Geometry, Groupoids, and Integrable Systems (Berkeley, 1989). Editors: P. Dazord and A. Weinstein. New York: Springer, 1991, 169–172. (Math. Sci. Res. Inst. Publ., 20.)
Eliashberg Ya. M., Ratiu T. The diameter of the symplectomorphism group is infinite. Invent. Math., 1991, 103(2), 327–340.
Schnirelmann A. I. The geometry of the group of diffeomorphisms and the dynamics of an ideal incompressible fluid. Math. USSR, Sb., 1987, 56(1), 79–105.
Schnirelmann A. I. Attainable diffeomorphisms. Geom. Funct. Anal., 1993, 3(3), 279–294.
1986-7 — M. L. Kontsevich
di Francesco P., Golinelli O., Guitter E. Meanders: exact asymptotic. Nucl. Phys. B, 2000, 570(3), 699–712. [Internet: http://www.arXiv.org/abs/cond-mat/9910453]
1986-7 — S. K. Lando
Arnold V. I. A branched covering ℂP2 → S4, hyperbolicity and projectivity topology. Sib. Math. J., 1988, 29(5), 717–726. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 431–448.]
di Francesco P., Golinelli O., Guitter E. Meanders and the Temperley-Lieb algebra. Commun. Math. Phys., 1997, 186(1), 1–59.
di Francesco P., Golinelli O., Guitter E. Meander, folding and arch statistics. Math. Comp. Modelling, 1997, 26(8–10), 97–147.
di Francesco P., Golinelli O., Guitter E. Meanders: exact asymptotics. Nucl. Phys. B, 2000, 570(3), 699–712. [Internet: http://www.arXiv.org/abs/cond-mat/9910453]
Jensen I., Guttman A. J. Critical exponents of plane meanders. Preprint, April 2000.
Lando S. K., Zvonkin A. K. Meanders. Selecta Math. Sov., 1992, 11(2), 117–144.
Lando S. K., Zvonkin A. K. Plane and projective meanders. Theor. Comp. Sci., 1993, 117(1–2), 227–241.
1986-8 — I. A. Bogaevsky, V. D. Sedykh
Bogaevsky I. A. Degree of smoothness for visible contours of convex hypersurfaces. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 119–127. (Adv. Sov. Math., 1.)
Bogaevsky I. A. Singularities of projective hypersurfaces. Funct. Anal. Appl., 1990, 24(2), 97–103.
Kiselman C. O. How smooth is the shadow of a smooth convex body? J. London Math. Soc., Ser. 2, 1986, 33(1), 101–109.
Sedykh V. D. An infinitely smooth compact convex hypersurface with a shadow whose boundary is not twice-differentiable. Funct. Anal. Appl., 1989, 23(3), 246–248.
1986-12 — B. A. Khesin
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
Bajer K. Flow kinematics and magnetic equilibria. Ph. D. Thesis, Cambridge University, 1989.
Etnyre J., Ghrist R. Contact topology and hydrodynamics: I. Beltrami fields and the Seifert conjecture. Nonlinearity, 2000, 13(2), 441–458.
Ginzburg V. L., Khesin B. A. Steady fluid flows and symplectic geometry. J. Geom. Phys., 1994, 14(2), 195–210.
Moffatt H. K. Some developments in the theory of turbulence. J. Fluid Mech., 1981, 106, 27–47.
Moffatt H. K. Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. I. Fundamentals. J. Fluid Mech., 1985, 159, 359–378.
Moffatt H. K. Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. II. Stability considerations. J. Fluid Mech., 1986, 166, 359–378.
Moffatt H. K. Structure and stability of solutions of the Euler equations: a Lagrangian approach. Phil. Trans. Roy. Soc. London, Ser. A, 1990, 333(1631), 321–342.
1987-3 — S. L. Tabachnikov
Arnold V. I. Huygens and Barrow, Newton and Hooke. Pioneers in Mathematical Analysis and Catastrophe Theory from Evolvents to Quasicrystals. Basel: Birkhäuser, 1990. [The Russian original 1989.]
Kasner E. Differential Geometric Aspects of Dynamics. AMS Colloq. Publ., 1913.
Nersessian A., Pogosyan G. Relation of the oscillator and Coulomb systems on spheres and pseudospheres. [Internet: http://www.arXiv.org/abs/quant-ph/0006118]
1987-3 — V. I. Arnold
Faure R. Méthodes d'intégration communes à la mécanique classique et à la mécanique ondulatoire. C. R. Acad. Sci. Paris, 1950, 230(4), 364–365.
Faure R. Transformations conformes en mécanique ondulatoire. C. R. Acad. Sci. Paris, 1953, 237, 603–605.
1987-4 — A. G. Khovanskiĭ, D. I. Novikov
Arnold V. I. A branched covering ℂP2 → S4, hyperbolicity and projectivity topology. Sib. Math. J., 1988, 29(5), 717–726. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 431–448.]
KhovanskiĬ A. G., Novikov D. I. Convex-concave body in \(\mathbb{R}\)P3 contains a line. [Internet: http://www.arXiv.org/abs/math.DG/0203200]
KhovanskiĬ A. G., Novikov D. I.L-convex-concave sets in real projective space and L-duality. [Internet: http://www.arXiv.org/abs/math.DG/0203203]
KhovanskiĬ A. G., Novikov D. I. On affine hypersurfaces with everywhere non-degenerate second quadratic form. [Internet: http://www.arXiv.org/abs/math.DG/0203202]
1987-6 — V. A. Vassiliev
Arnold V. I. Some topological invariants of algebraic functions. Trans. Moscow Math. Soc., 1970, 21, 30–52.
Arnold V. I. Spaces of functions with moderate singularities. Funct. Anal. Appl., 1989, 23(3), 169–177.
Vassiliev V. A. Topology of spaces of functions withoup compound singularities. Funct. Anal. Appl., 1989, 23(4), 277–286.
Vassiliev V. A. Topology of complements to discriminants and loop spaces, In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 9–21. (Adv. Sov. Math., 1.)
Vassiliev V. A. Complements of Discriminats of Smooth Maps: Topology and Applications. Providence, RI: Amer. Math. Soc., 1994. (Transl. Math. Monographs, 98.)
1987-7 — B. Z. Shapiro
Gusein-Zade S. M., Varchenko A. N. Verlinde algebras and the intersection form on vanishing cycles. Selecta Math (N. S.), 1997, 3(1), 79–97.
Kostov V. P., Shapiro B. Z. Flags in \(\mathbb{R}^3 \) transversal to a given set of flags form an M-manifold. Moscow Univ. Math. Bull., 1989, 44(5), 31–36.
Rietsch K. Intersections of Bruhat cells in real flag varieties. With an appendix by G. Lusztig. Internat. Math. Res. Notices, 1997, 13, 623–640.
Rietsch K. The intersection of opposed big cells in real flag varieties. Proc. Roy. Soc. London, Ser. A, 1997, 453(1959), 785–791.
Shapiro B. Z., Shapiro M. Z. The M-property of flag varieties. Topology Appl., 1992, 43(1), 65–81.
Shapiro B. Z., Shapiro M. Z., Vainshtein A. D. Topology of intersections of Schubert cells and Hecke algebra. Discrete Math., 1996, 153(1–3), 305–318.
Shapiro B. Z., Shapiro M. Z., Vainshtein A. D. On combinatorics and topology of pairwise intersections of Schubert cells in SLn/B. In: The Arnold-Gelfand Mathematical Seminars: Geometry and Singularity Theory. Editors: V. I. Arnold, I. M. Gelfand, V. S. Retakh and M. Smirnov. Boston, MA: Birkhäuser, 1997, 397–437.
Shapiro B. Z., Shapiro M. Z., Vainshtein A. D. Connected components in the intersection of two open opposite Schubert cells in SLn(\(\mathbb{R}\))/B. Internat. Math. Res. Notices, 1997, 10, 469–493.
Shapiro B. Z., Shapiro M. Z., Vainshtein A. D. Kazhdan-Lusztig polynomials for certain varieties of incomplete flags. Discrete Math., 1998, 180(1–3), 345–355.
Shapiro B. Z., Shapiro M. Z., Vainshtein A. D. Skew-symmetric vanishing lattices and intersections of Schubert cells. Internat. Math. Res. Notices, 1998, 11, 563–588.
Shapiro B. Z., Shapiro M. Z., Vainshtein A. D., Zelevinsky A. Simply laced Coxeter groups and groups generated by symplectic transvections. Michigan J. Math., 2000, 48, 531–552.
Shapiro B. Z., Vainshtein A. D. Euler characteristics for links of Schubert cells in the space of complete flags. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 273–286. (Adv. Sov. Math., 1.)
Zelevinsky A. Connected components of real double Bruhat cells. Internat. Math. Res. Notices, 2000, 21, 1131–1154.
1987-10 — V. N. Karpushkin
Karpushkin V. N. Topology of the zeros of eigenfunctions. Funct. Anal. Appl., 1989, 23(3), 218–220.
Karpushkin V. N. Multiplicities of singularities of eigenfunctions for the Laplace-Beltrami operator. Funct. Anal. Appl., 1995, 29(1), 62–64.
1987-12 — A. A. Bolibruch
Bolibruch A. A. On isomonodromic confluences of Fuchsian singularities. Proc. Steklov Inst. Math., 1998, 221, 117–132.
Bolibruch A. A. On orders of movable poles of the Schlesinger equation. J. Dynam. Control Systems, 2000, 6(1), 57–73.
Its A. R., Novokshenov V. Yu. The Isomonodromic Deformation Method in the Theory of Painlevé Equations. Berlin: Springer, 1986. (Lecture Notes in Math., 1191.)
Kostov V. P. On the existence of monodromy groups of Fuchsian systems on Riemann's sphere with unipotent generators. J. Dynam. Control Systems, 1996, 2(1), 125–155. [Prépublication Université de Nice, no. 401, septembre 1994.]
Malgrange B. Sur les déformations isomonodromiques: I. Singularités régulières. In: Mathématique et physique. Lectures presented at the seminar held at the École Normale Supérieure, Paris, 1979/1982. Editors: L. Boutet de Monvel, A. Douady and J.-L. Verdier. Boston, MA-Basel-Stuttgart: Birkhäuser, 1983, 401–426. (Progr. Math., 37.)
1987-14 — V. A. Vassiliev
Arnold V. I. Huygens and Barrow, Newton and Hooke. Pioneers in Mathematical Analysis and Catastrophe Theory from Evolvents to Quasicrystals. Basel: Birkhäuser, 1990. [The Russian original 1989.]
Arnold V. I., Vassiliev V. A. Newton's Principia read 300 years later. Notices Amer. Math. Soc., 1989, 36(9), 1148–1154; addendum: 1990, 37(2), 144.
Vassiliev V. A. Ramified Integrals, Singularities and Lacunas. Dordrecht: Kluwer Acad. Publ., 1995. (Math. Appl., 315.)
1988-3 — I. A. Bogaevsky
Arnold V. I. On the interior scattering of waves, defined by hyperbolic variational principles. J. Geom. Phys., 1988, 5(3), 305–315.
Arnold V. I. Surfaces defined by hyperbolic equations. Math. Notes, 1988, 44(1–2), 489–497. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 397–412.]
Arnold V. I. Singularities of Caustics and Wave Fronts. Dordrecht: Kluwer Acad. Publ., 1990. (Math. Appl., Sov. Ser., 62.)
Arnold V. I. Singularities of Caustics and Wave Fronts. Moscow: PHASIS, 1996 (in Russian). (Mathematician's Library, 1.)
1988-5 — Yu. M. Baryshnikov
Buckley S. Space-filling curves and related functions. Irish Math. Soc. Bull., 1996, 36, 9–18.
1988-6 — O. S. Kozlovskiĭ
Arnold V. I. Dynamics of intersections. In: Analysis, et cetera. Research papers published in honor of Jürgen Moser's 60th birthday. Editors: P. H. Rabinowitz and E. Zehnder. Boston, MA: Academic Press, 1990, 77–84.
Artin M., Mazur B. On periodic points. Ann. Math., Ser. 2, 1965, 81(1), 82–99.
Kaloshin V. Yu. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Commun. Math. Phys., 2000, 211(1), 253–271.
KozlovskiĬ O. S. The dynamics of intersections of analytic manifolds. Dokl. Math., 1992, 45(2), 425–427.
de Melo W., van Strien S. One-dimensional Dynamics. Berlin: Springer, 1993.
Misiurewicz M., Szlenk W. Entropy of piecewise monotone mappings. Studia Math., 1980, 67(1), 45–63.
1988-6 — M. B. Sevryuk
Arnold V. I. Dynamics of complexity of intersections. Bol. Soc. Brasil. Mat. (N. S.), 1990, 21(1), 1–10. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 489–499.]
Arnold V. I. Dynamics of intersections. In: Analysis, et cetera. Research papers published in honor of Jürgen Moser's 60th birthday. Editors: P. H. Rabinowitz and E. Zehnder. Boston, MA: Academic Press, 1990, 77–84.
Arnold V. I. Bounds for Milnor numbers of intersections in holomorphic dynamical systems. In: Topological Methods in Modern Mathematics. Proceedings of the symposium in honor of John Milnor's sixtieth birthday (Stony Brook, NY, 1991). Editors: L. R. Goldberg and A. V. Phillips. Houston, TX: Publish or Perish, 1993, 379–390.
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
Arnold V. I. Sur quelques problèmes de la théorie des systèmes dynamiques. Topol. Methods Nonlinear Anal., 1994, 4(2), 209–225. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 533–551.]
Artin M., Mazur B. On periodic points. Ann. Math., Ser. 2, 1965, 81(1), 82–99.
Kaloshin V. Yu. An extension of the Artin-Mazur theorem. Ann. Math., Ser. 2, 1999, 150(2), 729–741.
Kaloshin V. Yu. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Commun. Math. Phys., 2000, 211(1), 253–271.
KozlovskiĬ O. S. The dynamics of intersections of analytic manifolds. Dokl. Math., 1992, 45(2), 425–427.
Rosales-González E. On the growth of the numbers of periodic orbits of dynamical systems. Funct. Anal. Appl., 1991, 25(4), 254–262.
Rosales-González E. On the growth of the number of long period solutions of differential equations. Funct. Anal. Appl., 1992, 26(2), 99–105.
Rosales-González E. Milnor numbers in dynamical systems. In: Singularity Theory (Trieste, 1991). Editors: D. T. Lê, K. Saito and B. Teissier. River Edge, NJ: World Scientific, 1995, 627–634.
Rosales-González E. Intersection dynamics on Grassmann manifolds. Bol. Soc. Mat. Mexicana, Ser. 3, 1996, 2(2), 129–138.
1988-9 — V. A. Vassiliev
Arnold V. I. Spaces of functions with moderate singularities. Funct. Anal. Appl., 1989, 23(3), 169–177. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 455–469].
Eliashberg Ya. M., Mishachev N. M. Wrinkling of smooth mappings and its applications. Invent. Math., 1997, 130(2), 345–369.
Igusa K. Higher singularities of smooth functions are unnecessary. Ann. Math., Ser. 2, 1984, 119(1), 1–58.
Vassiliev V. A. Topology of spaces of functions without compound singularities. Funct. Anal. Appl., 1989, 23(4), 277–286.
Vassiliev V. A. Topology of complements to discriminants and loop spaces. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 9–21. (Adv. Sov. Math., 1.).
Vassiliev V. A. Complements of Discriminants of Smooth Maps: Topology and Applications, revised edition. Providence, RI: Amer. Math. Soc., 1994. (Transl. Math. Monographs, 98.)
1988-10 — V. A. Vassiliev
Arnold V. I. On some topological invariants of algebraic functions. Trans. Moscow Math. Soc., 1970, 21, 30–52.
Vassiliev V. A. Topology of complements to discriminants and loop spaces. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 9–21. (Adv. Sov. Math., 1.).
Vassiliev V. A. Complements of Discriminants of Smooth Maps: Topology and Applications, revised edition. Providence, RI: Amer. Math. Soc., 1994. (Transl. Math. Monographs, 98.)
1988-11 — V. D. Sedykh
Arnold V. I. Topological Invariants of Plane Curves and Caustics. Dean Jacqueline B. Lewis Memorial Lectures, Rutgers University. Providence, RI: Amer. Math. Soc., 1994. (University Lecture Series, 5.)
Arnold V. I. The geometry of spherical curves and the algebra of quaternions. Russian Math. Surveys, 1995, 50(1), 1–68.
Arnold V. I. Topological properties of Legendre projections in contact geometry of wave fronts. St. Petersburg Math. J., 1995, 6(3), 439–452.
Arnold V. I. On the number of flattening points of space curves. In: Sinaĭ's Moscow Seminar on Dynamical Systems. Editors: L. A. Bunimovich, B. M. Gurevich and Ya. B. Pesin. Providence, RI: Amer. Math. Soc., 1996, 11–22. (AMS Transl., Ser. 2, 171; Adv. Math. Sci., 28.)
Arnold V. I. Topological problems of the theory of wave propagation. Russian Math. Surveys, 1996, 51(1), 1–47.
Arnold V. I. Towards the Legendre Sturm theory of space curves. Funct. Anal. Appl., 1998, 32(2), 75–80.
Barner M. Über die Mindestanzahl stationärer Schmiegebenen bei geschlossenen streng-konvexen Raumkurven. Abh. Math. Semin. Univ. Hamburg, 1956, 20, 196–215.
Bisztriczky T. Inflectional convex space curves. Canad. J. Math., 1984, 36(3), 537–549.
Bose R. C. On the number of circles of curvature perfectly enclosing or perfectly enclosed by a closed convex oval. Math. Z., 1932, 35, 16–24.
Haupt O. Verallgemeinerung eines Satzes von R. C. Bose über die Anzahl der Schmiegkreise eines Ovals, die vom Oval umschlossen werden oder das Oval umschließen. J. Reine Angew. Math., 1969, 239/240, 339–352.
Kazarian M. E. The Chern-Euler number of circle bundle via singularity theory. Math. Scand., 1998, 82(2), 207–236.
Kazarian M. E. Relative Morse theory of one-dimensional bundles and cyclic homology. Funct. Anal. Appl., 1997, 31(1), 16–24.
Kneser A. Bemerkungen über die Anzahl der Extreme der Krümmung geschlossenen Kurven und über verwandte Fragen in einer nicht-euclidischen Geometrie. In: Festschrift H. Weber 70. Leipzig, 1912, 170–180.
Mohrmann H. Die Minimalzahl der stationären Ebenen eines räumlichen Ovals. Sitz. Ber. kgl. Bayerichen Akad. Wiss., Math.-Phys. Kl., 1917, 1–3.
Mukhopadhaya S. New methods in the geometry of a plane arc. I. Cyclic and sextactic points. Bull. Calcutta Math. Soc., 1909, 1, 31–37.
Romero-Fuster M. C. Convexly generic curves in \(\mathbb{R}^3 \). Geom. Dedicata, 1988, 28(1), 7–29.
Romero-Fuster M. C., Sedykh V. D. On the number of singularities, zero curvature points and vertices of a simple convex space curve. J. Geometry, 1995, 52(1–2), 168–172.
Romero-Fuster M. C., Sedykh V. D. A lower estimate for the number of zero-torsion points of a space curve. Beiträge zur Algebra und Geometrie, 1997, 38(1), 183–192.
Sedykh V. D. A theorem on four vertices of a convex space curve. Funct. Anal. Appl., 1992, 26(1), 28–32.
Sedykh V. D. Invariants of convex manifolds. Dokl. Math., 1993, 46(2), 392–396.
Sedykh V. D. Invariants of strictly convex manifolds. Funct. Anal. Appl., 1993, 27(3), 205–210.
Sedykh V. D. Connection of Lagrangian singularities with Legendre singularities under stereographic projection. Sb. Math., 1995, 83(2), 533–540.
Sedykh V. D. Invariants of nonflat manifolds. Funct. Anal. Appl., 1995, 29(3), 180–187.
Sedykh V. D. Strict convexity of a generic convex manifold. Proc. Steklov Inst. Math., 1995, 209, 174–190.
Sedykh V. D. Discrete versions of the four-vertex theorem. In: Topics in Singularity Theory. V. I. Arnold's 60th Anniversary Collection. Editors: A. Khovanskiĭ, A. Varchenko and V. Vassiliev. Providence, RI: Amer. Math. Soc., 1997, 197–207. (AMS Transl., Ser. 2, 180; Adv. Math. Sci., 34.)
Sedykh V. D. Invariants of submanifolds in Euclidean space. In: The Arnold-Gelfand Mathematical Seminars: Geometry and Singularity Theory. Editors: V. I. Arnold, I. M. Gelfand, V. S. Retakh and M. Smirnov. Boston, MA: Birkhäuser, 1997, 389–395.
Sedykh V. D. Some invariants of admissible homotopies of space curves. Funct. Anal. Appl., 2001, 35(4), 284–293.
Sedykh V. D. Relations between Euler numbers of manifolds of corank 1 singularities of a generic front. Dokl. Math., 2002, 65(2), 276–279.
Thorbergsson G., Umehara M. A unified approach to the four vertex theorems, II. In: Differential and Symplectic Topology of Knots and Curves. Editor: S. Tabachnikov. Providence, RI: Amer. Math. Soc., 1999, 229–252. (AMS Transl., Ser. 2, 190; Adv. Math. Sci, 42.)
Umehara M. A unified approach to the four vertex theorems, I. In: Differential and Symplectic Topology of Knots and Curves. Editor: S. Tabachnikov. Providence, RI: Amer. Math. Soc., 1999, 185–228. (AMS Transl., Ser. 2, 190; Adv. Math. Sci, 42.)
Uribe-Vargas R. On the (2k + 2)-vertex and (2k + 2)-flattening theorems in higher dimensional Lobatchevskian space. C. R. Acad. Sci. Paris, Sér. I Math., 1997, 325(5), 505–510.
1988-11 — R. Uribe-Vargas
Arnold V. I. The geometry of spherical curves and the algebra of quaternions. Russian Math. Surveys, 1995, 50(1), 1–68.
Arnold V. I. On the number of flattening points of space curves. In: Sinaĭ's Moscow Seminar on Dynamical Systems. Editors: L. A. Bunimovich, B. M. Gurevich and Ya. B. Pesin. Providence, RI: Amer. Math. Soc., 1996, 11–22. (AMS Transl., Ser. 2, 171; Adv. Math. Sci., 28.)
Barner M. Über die Mindestanzahl stationärer Schmiegeebenen bei geschlossenen streng-konvexen Raumkurven. Abh. Math. Semin. Univ. Hamburg, 1956, 20, 196–215.
Blaschke W. Vorlesungen über Differential-Geometrie, Vol. I, 3te Edition. Berlin: Springer, 1930.
Kazarian M. E. Nonlinear version of Arnold's theorem on flattening points. C. R. Acad. Sci. Paris, Sér. I Math., 1996, 323(1), 63–68.
Romero-Fuster M. C. Convexly generic curves in \(\mathbb{R}^3 \). Geom. Dedicata, 1988, 28(1), 7–29.
Sedykh V. D. A theorem on four vertices of a convex space curve. Funct. Anal. Appl., 1992, 26(1), 28–32.
Sedykh V. D. On some classes of curves in a projective space. In: Geometry and Topology of Caustics—CAUSTICS'98 (Warsaw). Editors: S. Janeczko and V. M. Zakalyukin. Warsaw: Polish Academy of Sciences, Institute of Mathematics, 1999, 237–266. (Banach Center Publ., 50.)
Segre B. Alcune proprietà differenziali in grande delle curve chiuse sghembe. Rend. Mat., Ser. 6, 1968, 1, 237–297.
Tabachnikov S. L. On zeros of the Schwarzian derivative. In: Topics in Singularity Theory. V. I. Arnold's 60th Anniversary Collection. Editors: A. Khovanskiĭ, A. Varchenko and V. Vassiliev. Providence, RI: Amer. Math. Soc., 1997, 229–239. (AMS Transl., Ser. 2, 180; Adv. Math. Sci., 34.)
Uribe-Vargas R. Symplectic and contact singularities in the differential geometry of curves and surfaces. Ph. D. Thesis, Université Paris 7, 2001, Ch. 3, § 7.
Uribe-Vargas R. Four-vertex theorems in higher-dimensional spaces for a larger class of curves than the convex ones. C. R. Acad. Sci. Paris, Sér. I Math., 2000, 330(12), 1085–1090.
1988-15 — R. Uribe-Vargas
Arnold V. I. Singularities of Caustics and Wave Fronts. Dordrecht: Kluwer Acad. Publ., 1990, § 2.4. (Math. Appl., Sov. Ser., 62.)
Arnold V. I. Sur les propriétés des projections Lagrangiennes en géométrie symplectique des caustiques. CEREMADE (UMR 7534), Université Paris-Dauphine, № 9320, 14/06/1993; Rev. Mat. Univ. Complut. Madrid, 1995, 8(1), 109–119. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 525–532.]
Chekanov Yu. V. Caustics in geometrical optics. Funct. Anal. Appl., 1986, 20(3), 223–226.
Kazarian M. E. Umbilical characteristic number of Lagrangian mappings of a 3-dimensional pseudo-optical manifold. J. Math. Sci., 1996, 32(5), 3672–3679.
Kazarian M. E. Umbilical characteristic number of Lagrangian mappings of 3-dimensional pseudo-optical manifolds. In: Singularities and Differential Equations (Warsaw, 1993). Editors: S. Janeczko, W. M. Zajączkowski and B. Ziemian. Warsaw: Polish Academy of Sciences, Institute of Mathematics, 1996, 161–170. (Banach Center Publ., 33.)
1988-23 — P. M. Akhmet'ev
Akhmet'ev P. M. Embedding of compacta, stable homotopy groups of spheres, and singularity theory. Russian Math. Surveys, 2000, 55(3), 405–462.
Arnold V. I. Cohomology classes of algebraic functions invariant under Tschirnhausen transformations. Funct. Anal. Appl., 1970, 4(1), 74–75. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 151–154.]
Arnold V. I. Topological invariants of algebraic functions, II. Funct. Anal. Appl., 1970, 4(2), 91–98.
Arnold V. I. Spaces of functions with moderate singularities. Funct. Anal. Appl., 1989, 23(3), 169–177. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 455–469].
Kazarian M. E. Characteristic classes of Lagrangian and Legendre singularities. Russian Math. Surveys, 1995, 50(4), 701–726.
Koschorke U. Vector Fields and Other Vector Bundle Morphisms—a Singularity Approach. Berlin: Springer, 1981. (Lecture Notes in Math., 847.)
Rimányi R., Szűcs A. Pontrjagin-Thom-type construction for maps with singularities. Topology, 1998, 37(6), 1177–1191.
Szűcs A. Cobordism groups of l-immersions, I; II. Acta Math. Acad. Sci. Hungar., 1976, 27(3–4), 343–358; 28(1–2), 93–102 (in Russian).
Szűcs A. Cobordism groups of immersions of oriented manifolds. Acta Math. Hungar., 1994, 64(2), 191–230.
Vassiliev V. A. Topology of Complements to Discriminants. Moscow: PHASIS, 1997 (in Russian).
1988-24 — S. V. Duzhin
Ilyushechkin N. V. On a certain class of smooth matrix-valued functions. Russian Math. Surveys, 1985, 40(1), 223–224.
Ilyushechkin N. V. The discriminant of the characteristic polynomial of a normal matrix. Math. Notes, 1992, 51(3), 230–235.
1988-24 — M. B. Sevryuk
Arnold V. I. Modes and quasimodes. Funct. Anal. Appl., 1972, 6(2), 94–101. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 189–202.]
Arnold V. I. Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect. Selecta Math. (N. S.), 1995, 1(1), 1–19. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 583–604.]
Arnold V. I. Mysterious Mathematical Trinities. Topological Economy Principle in Algebraic Geometry. Moscow: Moscow Center for Continuous Mathematical Education Press, 1997 (in Russian).
Arnold V. I. Relatives of the quotient of the complex projective plane by complex conjugation. Proc. Steklov Inst. Math., 1999, 224, 46–56. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
Arnold V. I. Symplectization, complexification and mathematical trinities. In: The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (Toronto, 1997). Editors: E. Bierstone, B. A. Khesin, A. G. Khovanskiĭ and J. E. Marsden. Providence, RI: Amer. Math. Soc., 1999, 23–37. (Fields Institute Commun., 24.); CEREMADE (UMR 7534), Université Paris-Dauphine, № 9815, 04/03/1998. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
Arnold V. I. Mysterious mathematical trinities. In: Students’ Readings in the Mathematical College of the Independent University of Moscow, Vol. 1. Editor: V. V. Prasolov. Moscow: Moscow Center for Continuous Mathematical Education Press, 2000, 4–16 (in Russian).
Arnold V. I. Polymathematics: is mathematics a single science or a set of arts? In: Mathematics: Frontiers and Perspectives. Editors: V. I. Arnold, M. Atiyah, P. Lax and B. Mazur. Providence, RI: Amer. Math. Soc., 2000, 403–416; CEREMADE (UMR 7534), Université Paris-Dauphine, № 9911, 10/03/1999. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
Arnold V. I. The complex Lagrangian Grassmannian. Funct. Anal. Appl., 2000, 34(3), 208–210.
Arnold V. I. The Lagrangian Grassmannian of a quaternionic hypersymplectic space. Funct. Anal. Appl., 2001, 35(1), 61–63.
Arnold V. I. Complexification of tetrahedron and pseudoprojective transformations. Funct. Anal. Appl., 2001, 35(4), 241–246.
Arnold V. I. Pseudoquaternion geometry. Funct. Anal. Appl., 2002, 36(1), 1–12.
Arnold V. I. The Geometry of Complex Numbers, Quaternions, and Spins. Moscow: Moscow Center for Continuous Mathematical Education Press, 2002 (in Russian).
Kazarian M. E. A remark on the eigenvectors and eigenvalues of hyper-Hermitian matrices. Preprint, 1998 (in Russian). [Internet: http://www.pdmi.ras.ru/~arnsem/papers/]
1988-25 — V. I. Arnold
Arnold V. I. Continued Fractions. Moscow: Moscow Center for Continuous Mathematical Education Press, 2001 (in Russian). (“Mathematical Education” Library, 14.)
Sturmfels B. Gröbner Bases and Convex Polytopes. Providence, RI: Amer. Math. Soc., 1996, 85–98. (University Lecture Series, 8.)
1988-26 — A. M. Leontovich
Conway J. H, Sloane N. J. A. Sphere Packings, Lattices and Groups, Vol. 1, 2. New York: Springer, 1988. (Grundlehren der Mathematischen Wissenschaften, 290.)
Rogers C. A. Packing and Covering. New York: Cambridge University Press, 1964. (Cambridge Tracts in Math. and Math. Phys., 54.)
1988-27
Arnold V. I. On some problems in symplectic topology. In: Topology and Geometry. Rohlin Seminar. Editor: O. Ya. Viro. Berlin: Springer, 1988, 1–5. (Lecture Notes in Math., 1346.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 425–429.
1988-28
Arnold V. I. On some problems in symplectic topology. In: Topology and Geometry. Rohlin Seminar. Editor: O. Ya. Viro. Berlin: Springer, 1988, 1–5. (Lecture Notes in Math., 1346.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 425–429.
1988-29
Arnold V. I. On some problems in symplectic topology. In: Topology and Geometry. Rohlin Seminar. Editor: O. Ya. Viro. Berlin: Springer, 1988, 1–5. (Lecture Notes in Math., 1346.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 425–429.
1988-30
Arnold V. I. On some problems in symplectic topology. In: Topology and Geometry. Rohlin Seminar. Editor: O. Ya. Viro. Berlin: Springer, 1988, 1–5. (Lecture Notes in Math., 1346.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 425–429.
1988-31
Arnold V. I. On some problems in symplectic topology. In: Topology and Geometry. Rohlin Seminar. Editor: O. Ya. Viro. Berlin: Springer, 1988, 1–5. (Lecture Notes in Math., 1346.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 425–429.
1988-32
Arnold V. I. On some problems in symplectic topology. In: Topology and Geometry. Rohlin Seminar. Editor: O. Ya. Viro. Berlin: Springer, 1988, 1–5. (Lecture Notes in Math., 1346.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 425–429.
1989-3 — V. A. Vassiliev
Vassiliev V. A. Complements of Discriminants of Smooth Maps: Topology and Applications, revised edition. Providence, RI: Amer. Math. Soc., 1994. (Transl. Math. Monographs, 98.)
1989-7 — S. M. Gusein-Zade
Arnold V. I. The longest curves of given degree and the quasicrystallic Harnack theorem in pseudoperiodic topology. Funct. Anal. Appl., 2002, 36(3), 165–171.
Esterov A. I. Densities of the Betti numbers of pre-level sets of quasi-periodic functions. Russian Math. Surveys, 2000, 55(2), 338–339.
Gusein-Zade S. M. Number of critical points for a quasiperiodic potential. Funct. Anal. Appl., 1989, 23(2), 129–130.
Gusein-Zade S. M. On the topology of quasiperiodic functions. In: Pseudoperiodic Topology. Editors: V. Arnold, M. Kontsevich and A. Zorich. Providence, RI: Amer. Math. Soc., 1999, 1–7. (AMS Transl., Ser.2, 197; Adv. Math. Sci., 46.)
1989-10 — V. I. Arnold (1989)
Arnold V. I. On the interior scattering of waves, defined by hyperbolic variational principles. J. Geom. Phys., 1988, 5(3), 305–315.
Arnold V. I. Singularities of Caustics and Wave Fronts. Dordrecht: Kluwer Acad. Publ., 1990, § 2.4. (Math. Appl., Sov. Ser., 62.)
1989-10 — I. A. Bogaevsky
Arnold V. I. On the interior scattering of waves, defined by hyperbolic variational principles. J. Geom. Phys., 1988, 5(3), 305–315.
Arnold V. I. Surfaces defined by hyperbolic equations. Math. Notes, 1988, 44(1), 489–497. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 397–412.]
Arnold V. I. Singularities of Caustics and Wave Fronts. Dordrecht: Kluwer Acad. Publ., 1990. (Math. Appl., Sov. Ser., 62.)
Arnold V. I. Singularities of Caustics and Wave Fronts. Moscow: PHASIS, 1996 (in Russian). (Mathematician's Library, 1.)
Bogaevsky I. A. Singularities of the propagation of short waves on the plane. Sb. Math., 1995, 186(11), 1581–1597.
Bogaevsky I. A. The interior scattering of rays and wave fronts on the plane. In: Arnold V. I. Singularities of Caustics and Wave Fronts. Moscow: PHASIS, 1996, § 8.5, 300–316 (in Russian). (Mathematician's Library, 1.)
Bogaevsky I. A. Singularities of short linear waves on the plane. In: The Arnold-Gelfand Mathematical Seminars: Geometry and Singularity Theory. Editors: V. I. Arnold, I. M. Gelfand, V. S. Retakh and M. Smirnov. Boston, MA: Birkhäuser, 1997, 107–112.
Braam P. J., Duistermaat J. J. Normal forms of real symmetric systems with multiplicity. Indag. Math. (N. S.), 1993, 4(4), 407–421.
Khesin B. A. Singularities of light hypersurfaces and structure of hyperbolicity sets for systems of partial differential equations. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 119–127. (Adv. Sov. Math., 1.)
1989-11 — M. B. Mishustin
Arnold V. I. Bifurcations of invariant manifolds of differential equations and normal forms of neighborhoods of elliptic curves. Funct. Anal. Appl., 1976, 10(4), 249–259.
Arnold V. I. Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd edition. New York: Springer, 1988. (Grundlehren der Mathematischen Wissenschaften, 250.) [The Russian original 1978.]
Grauert H. Über modifikationen und exzeptionelle analytische Mengen. Math. Ann., 1962, 146(4), 331–368.
Il'yashenko Yu. S. Positive type embeddings of elliptic curves into complex surfaces. Trudy Moskov. Mat. Obshch., 1982, 45, 37–67 (in Russian, for the English translation see Trans. Moscow Math. Soc.)
Il'yashenko Yu. S., Pyartli A. S. Neighborhoods of zero type in embedded complex tori. Trudy Semin. Petrovskogo, 1979, 5, 85–90 (in Russian). [The English translation in: Topics in Modern Mathematics. Editor: O. A. Oleĭnik. New York: Consultant Bureau, 1985, 107–121. (Petrovskiĭ Semin., 5.)]
Il'yashenko Yu. S., Pyartli A. S. Materialization of Poincaré resonances and divergence of normalizing series. Trudy Semin. Petrovskogo, 1981, 7, 3–49 (in Russian). [The English translation: J. Sov. Math., 1985, 31, 3053–3092.]
Kosarew S. Modulräume holomorpher Abbildungen auf konkaven komplexen Räumen. Ann. Sci. École Norm. Super., Ser. 4, 1987, 20(3), 285–310.
Mishustin M. B. Neighborhoods of Riemann curves in complex spaces. Funct. Anal. Appl., 1995, 29(1), 20–31.
Savel'ev V. I. Zero-type embeddings of the sphere into complex surfaces. Moscow Univ. Math. Bull., 1982, 37(4), 34–39.
1989-14 — V. A. Vassiliev
Arnold V. I., Vassiliev V. A., Goryunov V. V., Lyashko O. V. Singularities. I. Local and Global Theory. Berlin: Springer, 1993, Sect. 3.3. (Encyclopædia Math. Sci., 6; Dynamical Systems, VI.) [The Russian original 1988.]
Shastri A. R. Polynomial representations of knots. Tôhoku Math. J., Ser. 2, 1992, 44(1), 11–17.
Vassiliev V. A. On spaces of polynomial knots. Sb. Math., 1996, 187(2), 193–213.
1989-15
Arnold V. I., Vishik M. I., Il'yashenko Yu. S., Kalashnikov A. S., Kondrat'ev V. A., Kruzhkov S. N., Landis E. M., Millionshchikov V. M., OleĬnik O. A., Filippov A. F., Shubin M. A. Some unsolved problems in the theory of differential equations and mathematical physics. Uspekhi Mat. Nauk, 1989, 44(4), 191–202 (in Russian). [The English translation: Russian Math. Surveys, 1989, 44(4), 157–171.]
The Russian original of the section “Problems by V. I. Arnold” (Uspekhi Mat. Nauk, 1989, 44(4), p. 191–192) is reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 471–472.
1989-16
Arnold V. I., Vishik M. I., Il'yashenko Yu. S., Kalashnikov A. S., Kondrat'ev V. A., Kruzhkov S. N., Landis E. M., Millionshchikov V. M., OleĬnik O. A., Filippov A. F., Shubin M. A. Some unsolved problems in the theory of differential equations and mathematical physics. Uspekhi Mat. Nauk, 1989, 44(4), 191–202 (in Russian). [The English translation: Russian Math. Surveys, 1989, 44(4), 157–171.]
The Russian original of the section “Problems by V. I. Arnold” (Uspekhi Mat. Nauk, 1989, 44(4), p. 191–192) is reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 471–472.
1989-17
Arnold V. I., Vishik M. I., Il'yashenko Yu. S., Kalashnikov A. S., Kondrat'ev V. A., Kruzhkov S. N., Landis E. M., Millionshchikov V. M., OleĬnik O. A., Fllippov A. F., Shubin M. A. Some unsolved Problems in the theory of differential equations and mathematical physics. Uspekhi Mat. Nauk, 1989, 44(4), 191–202 (in Russian). [The English transhtion: Russicm Math. Surveys, 1989, 44(4), 157–171.]
The Russian original of the section “Problems by V. I. Arnold” (Uspekhi Mat. Nauk, 1989, 44(4), p. 191–192) is reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 471–472.
1989-18
Arnold V. l., Vishik M. I., Il'yashenko Yu. S., Kalashnikov A. S., Kondrat'ev V. A., Kruzhkov S. N., Landis E. M., Millionshchikov V. M., OleĬnik O. A., Filippov A. F., Shubin M. A. Some unsolved problems in the theory of differential equations and mathematical physics. Uspekhi Mat. Nauk, 1989, 44(4), 191–202 (in Russian). [The English translation: Russian Math. Surveys, 1989, 44(4), 157–171.]
The Russian original of the section “Problems by V. I. Arnold” (Uspekhi Mat. Nauk, 1989, 44(4), p. 191–192) is reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 471–472.
1989-19
Arnold V. l., Vishik M. I., Il'yashenko Yu. S., Kalashnikov A. S., Kondrat'ev V. A., Kruzhkov S. N., Landis E. M., Millionshchikov V. M., OleĬnik O. A., Filippov A. F., Shubin M. A. Some unsolved problems in the theory of differential equations and mathematical physics. Uspekhi Mat. Nauk, 1989, 44(4), 191–202 (in Russian). [The English translation: Russian Math. Surveys, 1989, 44(4), 157–171.]
The Russian original of the section “Problems by V. I. Arnold” (Uspekhi Mat. Nauk, 1989, 44(4), p. 191–192) is reprinted in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 471–472.
1989-20 — V. P. Kostov
Kostov V. P. On the stratification and singularities of the Stokes hypersurface of one-and two-parameter families of polynomials. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 251–271. (Adv. Sov. Math., 1.)
1990-1
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1990-11 — F. Aicardi
Aicardi F. Sur le découpage de domaines bornés de dimension N. C. R. Acad. Sci. Paris, Sér. I Math., 1993, 316(2), 175–181.
1990-11 — A. M. Leontovich
From A. D. Sakharov's “amateur problems”. Kvant, 1991, № 5, 11–12 (in Russian).
Leontovich A. M., Maresin V. M., Ogaryshev V. F., Philippov V. B. Models of formation of a one-layer tissue. In: Theoretical and Mathematical Aspects of Morphogenesis. Moscow: Nauka, 1987, 182–198 (in Russian).
1990-11 — B. T. Polyak
Pólya G. Mathematics and Plausible Reasoning. Vol. I. Induction and Analogy in Mathematics. Princeton, NJ: Princeton University Press, 1954. [Reprinted 1990.]
Schläfli L. Gesammelte mathematische Abhandlungen, Band 1. Basel: Birkhäuser, 1950.
Winder R. O. Partitions of N-space by hyperplanes. SIAM J. Appl. Math., 1966, 14(4), 811–818.
1990-12 — V. A. Vassiliev
Arnold V. I. A branched covering \(\mathbb{C}\)P2 → S4, hyperbolicity and projectivity topology. Sib. Math. J., 1988, 29(5), 717–726. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 431–448.]
Blum L., Shub M., Smale S. On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal mashines. Bull. Amer. Math. Soc. (N. S.), 1989, 21(1), 1–46.
Vassiliev V. A. A geometric realization of the homology of classical Lie groups, and complexes S-dual to flag manifolds. St. Petersburg Math. J., 1991, 3(4), 809–815.
1990-14 — B. A. Khesin
Arnold V. I. The asymptotic Hopf invariant and its applications. In: Proceedings of the All-Union School on Differential Equations with Infinitely Many Independent Variables and on Dynamical Systems with Infinitely Many Degrees of Freedom (Dilizhan, May 21–June 3, 1973). Yerevan: AS of Armenian SSR, 1974, 229–256 (in Russian). [The English translation: Selecta Math. Sov., 1986, 5(4), 327–345.] [The Russian original is reprinted and supplemented in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 215–236.]
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
Eliashberg Ya. M., Givental A. B., Hofer H. Introduction to symplectic field theory. Geom. Funct. Anal., 2000, Special Volume, Part II, 560–673.
1990-16 — B. A. Khesin
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
Verjovsky A., Vila Freyer R. F. The Jones-Witten invariant for flows on a 3-dimensional manifold. Commun. Math. Phys., 1994, 163(1), 73–88.
1990-17
Arnold V. I. Ten problems. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 1–8. (Adv. Sov. Math., 1.)
1990-18
Arnold V. I. Ten problems. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 1–8. (Adv. Sov. Math., 1.)
1990-19
Arnold V. I. Ten problems. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 1–8. (Adv. Sov. Math., 1.)
1990-20
Arnold V. I. Ten problems. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 1–8. (Adv. Sov. Math., 1.)
1990-21
Arnold V. I. Ten problems. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 1–8. (Adv. Sov. Math., 1.)
1990-22
Arnold V. I. Ten problems. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 1–8. (Adv. Sov. Math., 1.)
1990-22 — M. B. Mishustin
Mishustin M. B. Neighborhoods of the Riemann sphere in complex surfaces. Funct. Anal. Appl., 1993, 27(3), 176–185.
1990-23
Arnold V. I. Ten problems. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 1–8. (Adv. Sov. Math., 1.)
1990-24
Arnold V. I. Ten problems. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 1–8. (Adv. Sov. Math., 1.)
1990-25
Arnold V. I. Ten problems. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 1–8. (Adv. Sov. Math., 1.)
1990-26
Arnold V. I. Ten problems. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 1–8. (Adv. Sov. Math., 1.)
1990-27
Arnold V. I. Ten problems. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 1–8. (Adv. Sov. Math., 1.)
1990-28
Arnold V. I. Ten problems. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 1–8. (Adv. Sov. Math., 1.)
1991-3
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1991-3 — V. I. Arnold (1991)
Arnold V. I. Bounds for Milnor numbers of intersections in holomorphic dynamical systems. In: Topological Methods in Modern Mathematics. Proceedings of the symposium in honor of John Milnor's sixtieth birthday (Stony Brook, NY, 1991). Editors: L. R. Goldberg and A. V. Phillips. Houston, TX: Publish or Perish, 1993, 379–390.
1991-3 — S. V. Duzhin
Beukers F. The zero-multiplicity of ternary recurrences. Compos. Math., 1991, 77(2), 165–177.
Deshommes B. Puissances binomiales dans un corps cubique. Dissertationes Math. (Rozprawy Mat.), 1991, 312, 57 pp.
1991-8 — M. B. Sevryuk
Rosales-González E. Intersection dynamics on Grassmann manifolds. Bol. Soc. Mat. Mexicana, Ser. 3, 1996, 2(2), 129–138.
1991-10
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1991-11 — V. I. Arnold
Arnold V. I. Higher dimensional continued fractions. Reg. Chaot. Dynamics, 1998, 3(3), 10–17.
Korkina E. I. La périodicité des fractions continues multidimensionnelles. C. R. Acad. Sci. Paris, Sér. I Math., 1994, 319(8), 777–780.
1991-11 — J.-O. Moussafir
Arnold V. I. Continued Fractions. Moscow: Moscow Center for Continuous Mathematical Education Press, 2001 (in Russian). (“Mathematical Education” Library, 14.)
Brodén T. Wahrscheinlichkeits bestimmungen bei der gewöhnlichen Kettenbruchentwicklung reeller Zahlen. Akad. Föhr. Stockholm, 1900, 57, 239–266.
Kontsevich M. L., Sukhov Yu. M. Statistics of Klein polyhedra and multidimensional continued fractions. In: Pseudoperiodic Topology. Editors: V. Arnold, M. Kontsevich and A. Zorich. Providence, RI: Amer. Math. Soc., 1999, 9–27. (AMS Transl., Ser. 2, 197; Adv. Math. Sci., 46.)
Korkina E. I. La périodicité des fractions continues multidimensionnelles. C. R. Acad. Sci. Paris, Sér. I Math., 1994, 319(8), 777–780.
Korkina E. I. Two-dimensional continued fractions. The simplest examples. Proc. Steklov Inst. Math., 1995, 209, 124–144.
Moussafir J.-O. Voiles et polyédres de Klein. Géométrie, algorithmes et statistiques. Thèse, Université Paris-Dauphine, 2000.
Tsuchihashi H. Higher-dimensional analogues of periodic continued fractions and cusp singularities. Tôhoku Math. J., Ser. 2, 1983, 35(4), 607–639.
Wiman A. Über eine-wahrscheinlichkeits Auflage bei Kettenbruchentwicklungen. Akad. Föhr. Stockholm, 1900, 57, 589–841.
1991-14
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1991-14 — A. V. Zorich
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
Dynnikov I. A. Proof of S. P. Novikov's conjecture on the semiclassical motion of an electron. Math. Notes, 1993, 53(5), 495–501.
Dynnikov I. A. Semi-classical motion of the electron. Proof of Novikov's conjecture in general position and counterexamples. In: Solitons, Geometry, and Topology: on the Crossroad. Editors: V. M. Buchstaber and S. P. Novikov. Providence, RI: Amer. Math. Soc. 1997, 45–73. (AMS Transl., Ser. 2, 179; Adv. Math. Sci., 33.)
Dynnikov I. A. Surfaces in 3-torus: geometry of plane sections. In: Papers from the 2nd European Congress of Mathematics (Budapest, 1996), Vol. 1. Editors: A. Balog, G. O. H. Katona, A. Recski and D. Szász. Basel: Birkhäuser, 1998, 162–177. (Progr. Math., 168.)
Dynnikov I. A. The geometry of stability zones in Novikov's problem on the semi-classical motion of an electron. Russian Math. Surveys, 1999, 54(1), 21–59.
Novikov S. P. The Hamiltonian formalism and a multi-valued analogue of Morse theory. Russian Math. Surveys, 1982, 37(5), 1–56.
Novikov S. P. Quasiperiodic structures in topology. In: Topological Methods in Modern Mathematics. Proceedings of the symposium in honor of John Milnor's sixtieth birthday (Stony Brook, NY, 1991). Editors: L. R. Goldberg and A. V. Phillips. Houston, TX: Publish or Perish, 1993, 223–233.
Novikov S. P. The semiclassical electron in a magnetic field and lattice. Some problems of low dimensional “periodic” topology. Geom. Funct. Anal., 1995, 5(2), 434–444.
Novikov S. P., Mal'tsev A. Ya. Topological phenomena in normal metals. Letters to JETP, 1996, 63(10), 809–813; Physics-Uspekhi, 1998, 41(3), 231–239. [Internet: http://www.arXiv.org/abs/cond-mat/9709007]
Zorich A. V. S. P. Novikov's problem on the semiclassical motion of an electron in a homogeneous magnetic field that is close to rational. Russian Math. Surveys, 1984, 39(5), 287–288.
Zorich A. V. Asymptotic flag of an orientable measured foliation on a surface. In: Geometric Study of Foliations (Tokyo, 1993). Editors: T. Mizutani, K. Masuda, S. Matsumoto, T. Inaba, T. Tsuboi and Y. Mitsumatsu. River Edge, NJ: World Scientific, 1994, 479–498.
1992-1
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1992-1 — S. M. Gusein-Zade
Gusein-Zade S. M. On a problem of B. Teissier. In: Topics in Singularity Theory. V. I. Arnold's 60th Anniversary Collection. Editors: A. Khovanskiĭ, A. Varchenko and V. Vassiliev. Providence, RI: Amer. Math. Soc., 1997, 117–125. (AMS Transl., Ser. 2, 180; Adv. Math. Sci., 34.)
Gusein-Zade S. M. On the existence of deformations without critical points (the Teissier problem for functions of two variables). Funct. Anal. Appl., 1997, 31(1), 58–60.
1992-3
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1992-7
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1992-8 — B. A. Khesin
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
Brylinski J.-L. Loop Spaces, Characteristic Classes and Geometric Quantization. Boston, MA: Birkhäuser, 1993. (Progr. Math., 107.)
1992-13 — V. Yu. Kaloshin
Artin M., Mazur B. On periodic points. Ann. Math., Ser. 2, 1965, 81(1), 82–99.
Bonatti C., Díaz L. Connexions hétéroclines et généricité d'une infinité de puits et de sources. Ann. Sci. École Norm. Sup. (4), 1999, 32(1), 135–150.
Bowen R. On Axiom A Diffeomorphisms. Providence, RI: Amer. Math. Soc., 1978. (Regional Conf. Ser. in Math., 35.)
Gonchenko S. V., Shil'nikov L. P., Turaev D. V. On models with nonrough Poincaré homoclinic curves. Physica D, 1993, 62(1–4), 1–14.
Hunt B. R., Sauer T., Yorke J. A. Prevalence: a translation-invariant “almost every” for infinite-dimensional spaces. Bull. Amer. Math. Soc. (N. S.), 1992, 27(2), 217–238; addendum: 1993, 28(2), 306–307.
Kaloshin V. Yu. Some prevalent properties of smooth dynamical systems. Proc. Steklov Inst. Math., 1996, 213, 115–140.
Kaloshin V. Yu. An extension of the Artin-Mazur theorem. Ann. Math., Ser. 2, 1999, 150(2), 729–741.
Kaloshin V. Yu. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Commun. Math. Phys., 2000, 211(1), 253–271.
Kaloshin V. Yu. A stretched exponential estimate on growth of number of periodic points for diffeomorphisms with probability one. Ph. D. Thesis, Princeton University, 2001.
Kaloshin V. Yu., Hunt B. R. A stretched exponential estimate on growth of number of periodic points for diffeomorphisms with probability one, I; II. Electron. Res. Announc. Amer. Math. Soc., 2001, 7, 17–27; 28–36 (electronic).
Kaloshin V. Yu., KozlovskiĬ O. S. A Cr-unimodal map with a superexponential growth of the number of periodic points. Preprint.
Newhouse S. Diffeomorphisms with infinitely many sinks. Topology, 1974, 13, 9–18.
Oxtoby J. Measure and Category. A Survey of the Analogies Between Topological and Measure Spaces, 2nd edition. New York-Berlin: Springer, 1980. (Graduate Texts in Math., 2.)
Pujals E. R., Sambarino M. Homoclinic tangencies and hyperbolicity for surface diffeomorphisms. Ann. Math., Ser. 2, 2000, 151(3), 961–1023.
Rosales-González E. Growth of periodic orbits of dynamical systems. Funct. Anal. Appl., 1991, 25(4), 254–262.
Simon B. Operators with singular continuous spectrum. I. General operators. Ann. Math., Ser. 2, 1995, 141(1), 131–145.
Smale S. Differentiable dynamical systems. Bull. Amer. Math. Soc., 1967, 73, 747–817.
Vishik M. I., Kuksin S. B. Quasilinear elliptic equations and Fredholm manifolds. Moscow Univ. Math. Bull., 1985, 40(6), 26–34.
Yomdin Y. A quantitative version of the Kupka-Smale theorem. Ergod. Theory Dynam. Systems, 1985, 5(3), 449–472.
1992-14
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1992-15
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1993-3 — R. Uribe-Vargas
Uribe-Vargas R. Symplectic and contact singularities in the differential geometry of curves and surfaces. Ph. D. Thesis, Université Paris 7, 2001, Ch. 6.
1993-5 — J.-O. Moussafir
Arnold V. I. A-graded algebras and continued fractions. Commun. Pure Appl. Math., 1989, 42(7), 993–1000. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 473–482.]
Fulton W. Introduction to Toric Varieties. Princeton, NJ: Princeton University Press, 1993. (Ann. Math. Studies, 131.)
Sturmfels B. Gröbner bases of toric varieties. Tôhoku Math. J., Ser. 2, 1991, 43(2), 249–261.
Sturmfels B. Gröbner Bases and Convex Polytopes. Providence, RI: Amer. Math. Soc., 1996. (University Lecture Series, 8.)
1993-6 — S. V. Chmutov
Fintushel R., Stern R. J. Instanton homology of Seifert fibred homology three-spheres. Proc. London Math. Soc., Ser. 3, 1990, 61(1), 109–137.
1993-11 — M. B. Sevryuk
Arnold V. I. Higher dimensional continued fractions. Reg. Chaot. Dynamics, 1998, 3(3), 10–17.
Kontsevich M. L., Sukhov Yu. M. Statistics of Klein polyhedra and multidimensional continued fractions. In: Pseudoperiodic Topology. Editors: V. Arnold, M. Kontsevich and A. Zorich. Providence, RI: Amer. Math. Soc., 1999, 9–27. (AMS Transl., Ser. 2, 197; Adv. Math. Sci., 46.)
Arnold V. I. Continued Fractions. Moscow: Moscow Center for Continuous Mathematical Education Press, 2001 (in Russian). (“Mathematical Education” Library, 14.)
Arnold V. I.A-graded algebras and continued fractions. Commun. Pure Appl. Math., 1989, 42(7), 993–1000. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 473–482.]
1993-11 — V. I. Arnold
Avdeeva M. O., BykovskiĬ V. A. A solution of Arnold's problem on the Gauss-Kuz'min statistics. Preprint № 8, Far Eastern Branch of Russian Academy of Sciences, Institute for Applied Mathematics, Khabarovsk Division. Vladivostok: Dal'nauka, 2002, 12 pp. (in Russian).
1993-13 — V. I. Arnold (1993)
Perron B., Vannier J.-P. Groupe de monodromie géométrique des singularités simples. C. R. Acad. Sci. Paris, Sér. I Math., 1992, 315(10), 1067–1070.
1993-13 — S. V. Chmutov
Wajnryb B. Artin groups and geometric monodromy. Invent. Math., 1999, 138(3), 563–571.
1993-17 — V. I. Arnold
Arnold V. I. Fermat dynamics, matrix arithmetics, finite circles and finite Lobachevsky planes. Funct. Anal. Appl., 2004, 38(1), 20 pp.
Remila É. Sur le pavage de tore Ta×b par hm et vn. C. R. Acad. Sci. Paris, Sér. I Math., 1993, 316(9), 949–952.
1993-20 — V. I. Arnold (1993)
Fintushel R., Stern R. J. Integer graded instanton homology groups for homology three-spheres. Topology, 1992, 31(3), 589–604.
Lescop C. Sur l'invariant de Casson-Walker: formule de chirurgie globale et généralisation aux variétés de dimension 3 fermées orientées. C. R. Acad. Sci. Paris, Sér. I Math., 1992, 315(4), 437–440.
1993-24 — V. I. Arnold
Arnold V. I. Singularities of Caustics and Wave Fronts. Dordrecht: Kluwer Acad. Publ., 1990. (Math. Appl., Sov. Ser., 62.)
Napolitano F. Duality between the generalized caustic and Maxwell stratum for the singularities B2k and C2k . C. R. Acad. Sci. Paris, Sér. I Math., 1997, 325(3), 313–317.
Varchenko A. N., Givental A. B. Mapping of periods and intersection form. Funct. Anal. Appl., 1982, 16(2), 83–93.
1993-25 — B. S. Kruglikov
Arnold V. I. Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd edition. New York: Springer, 1988. (Grundlehren der Mathematischen Wissenschaften, 250.) [The Russian original 1978.]
Bangert V. Existence of a complex line in tame almost complex tori. Duke Math. J., 1998, 94(1), 29–40.
Gromov M. L. Pseudoholomorphic curves in symplectic manifolds. Invent. Math., 1985, 82(2), 307–347.
Kruglikov B. S., Overholt M. The Kobayashi pseudodistance on almost complex manifolds. Differ. Geom. Appl., 1999, 11, 265–277. [Internet: http://www.arXiv.org/abs/math.DG/9703005]
Kruglikov B. S. Nijenhuis tensors and obstructions to constructing pseudoholomorphic mappings. Math. Notes, 1998, 63(4), 476–493.
Kruglikov B. S. Existence of close pseudoholomorphic disks for almost complex manifolds and their application to the Kobayashi-Royden pseudonorm. Funct. Anal. Appl., 1999, 33(1), 38–48.
Kuksin S. B. Pseudoholomorphic 2-tori in T4. Differ. Geom. Appl., 1996, 6(2), 109–119.
McDuff D., Salamon D.J-Holomorphic Curves and Quantum Cohomology. Providence, RI: Amer. Math. Soc., 1994. (University Lecture Series, 6.)
Moser J. On the persistence of pseudoholomorphic curves on an almost complex torus (with an appendix by PÖSCHEL J.). Invent. Math., 1995, 119(3), 401–442.
Nijenhuis A., Woolf W. B. Some integration problems in almost-complex and complex manifolds. Ann. Math., Ser. 2, 1963, 77(3), 424–489.
1993-27 — F. Napolitano
Napolitano F. Pseudo-homology of complex hypersurfaces. C. R. Acad. Sci. Paris, Sér. I Math., 1999, 328(11), 1025–1030.
1993-28 — V. I. Arnold (1993)
Griffiths P. Exterior Differential Systems and the Calculus of Variations. Boston, MA: Birkhäuser, 1983. (Progr. Math., 25.)
1993-28 — B. S. Kruglikov
Krasil'shchik I. S., Lychagin V. V., Vinogradov A. M. Geometry of Jet Spaces and Nonlinear Partial Differential Equations. New York: Gordon and Breach, 1986. (Adv. Studies in Contemp. Math., 1.)
Krishchenko A. P. The structure of the singularities of the solutions of quasilinear equations. Uspekhi Mat. Nauk, 1976, 31(3), 219–220 (in Russian).
Krishchenko A. P. On the bends of R-manifolds. Moscow Univ. Math. Bull., 1977, 32(1), 13–16.
Lychagin V. V. Singularities of multivalued solutions of nonlinear differential equations, and nonlinear phenomena. Acta Appl. Math., 1985, 3(2), 135–173.
Lychagin V. V. Geometric theory of singularities of solutions of nonlinear differential equations. In: Itogi Nauki i Tekhniki VINITI. Problems in Geometry, Vol. 20. Moscow: VINITI, 1988, 207–247 (in Russian). [The English translation: J. Sov. Math., 1990, 51(6), 2735–2757.]
Rakhimov A. Kh. Singularities of Riemannian invariants. Funct. Anal. Appl., 1993, 27(1), 39–50.
Spencer D. C. Overdetermined systems of linear partial differential equations. Bull. Amer. Math. Soc., 1969, 75, 179–239.
1993-29 — A. A. Glutsyuk
Barabanov N. E. On the Kalman problem. Sib. Math. J., 1988, 29(3), 333–341.
Bernat J., Llibre J. Counterexample to Kalman and Markus-Yamabe conjecture in dimension larger than 3. Dynam. Contin. Discrete Impuls. Systems, 1996, 2(3), 337–379.
Chen P. N., He J. X., Qin H. S. A proof of the Jacobian conjecture on global asymptotic stability. Chinese Sci. Bull., 1996, 41(15), 1233–1237.
Chen P. N., He J. X., Qin H. S. A proof of the Jacobian conjecture on global asymptotic stability. Acta Math. Sinica (Engl. Ser.), 2001, 17(1), 119–132.
Cima A., van den Essen A., Gasull A., Hubbers E., Mañosas F. A polynomial counterexample to the Markus-Yamabe conjecture. Rep. 9551, Dept. Math. Univ. Nijmegen, Nijmegen, 1995.
Cima A., van den Essen A., Gasull A., Hubbers E., Mañosas F. A polynomial counterexample to the Markus-Yamabe conjecture. Adv. Math., 1997, 131(2), 453–457.
Fessler R. A solution to the global asymptotic stability Jacobian conjecture and a generalization. In: Recent Results on the Global Asymptotic Stability Jacobian Conjecture (Editor: M. Sabatini), Matematica 429, Università di Trento, 1994. Workshop, I-38050 POVO (TN) Italy, September 14–17, 1993.
Fessler R. A proof of the two-dimensional Markus-Yamabe stability conjecture and a generalization. Ann. Polon. Math., 1995, 62(1), 45–74.
Glutsyuk A. A. A complete solution of the Jacobian problem for vector field on the plane. Russian Math. Surveys, 1994, 49(3), 185–186.
Glutsyuk A. A. Asymptotic stability of linearizations of a planar vector field with a singular point implies global stability. Funct. Anal. Appl., 1995, 29(4), 238–247.
Glutsyuk A. A. A three-dimensional counterexample to the Markus-Yamabe global stability problem. Uspekhi Mat. Nauk, 1996, 51(5), 169 (in Russian).
Glutsyuk A. A. Asymptotic stability of linearizations of a vector field in \(\mathbb{R}^3 \) with a singular point does not imply global stability. Preprint, Comunicaciónes del CIMAT, Guanajuato, Mexico, 1996.
Gutiérrez C. A solution to the bidimensional global asymptotic stability conjecture. In: Recent Results on the Global Asymptotic Stability Jacobian Conjecture (Editor: M. Sabatini), Matematica 429, Università di Trento, 1994. Workshop, I-38050 POVO (TN) Italy, September 14–17, 1993.
Gutiérrez C. A solution to the bidimensional global asymptotic stability conjecture. Ann. Institut Henri Poincaré, Analyse non linéaire, 1995, 12(6), 627–671.
Hartman P. Ordinary Differential Equations. New York-London-Sydney: John Wiley, 1964, Ch. XIV, Part III.
Markus L., Yamabe H. Global stability criteria for differential systems. Osaka Math. J., 1960, 12, 305–317.
Meisters G. H. Featured Review 98c:34079. Math. Reviews, 1998.
Meisters G. H. Featured Review 98c:34080. Math. Reviews, 1998.
Meisters G. H. Featured Review 98k:34084. Math. Reviews, 1998.
Meisters G. H., Olech C. Solution of the global asymptotic stability Jacobian conjecture for the polynomial case. In: Analyse Mathématique et Applications (Contributions en l'honneur de J.-L. Lions). Paris: Gauthier-Villars, 1988, 373–381.
Olech C. On the global stability of an autonomous system on the plane. Contrib. Differ. Equations, 1963, 1(3), 389–400.
Olech C. Featured Review 96k:34099a,b,c. Math. Reviews, 1996.
Parthasarathy T., Sabatini M. Some new results on the global asymptotic stability Jacobian conjecture. Bull. Polish Acad. Sci. Math., 1993, 41(3), 221–228 (1994).
1993-30 — Yu. M. Baryshnikov
Baryshnikov Yu. M. Bifurcation diagrams of quadratic differentials. C. R. Acad. Sci. Paris, Sér. I Math., 1997, 325(1), 71–76.
Baryshnikov Yu. M. On Stokes sets. In: New Developments in Singularity Theory (Cambridge, 2000). Editors: D. Siersma, C. T. C. Wall and V. M. Zakalyukin. Dordrecht: Kluwer Acad. Publ., 2001, 65–86 (NATO Sci. Ser. II Math. Phys. Chem., 21.)
Berry M. V. Stokes’ phenomenon; smoothing a Victorian discontinuity. Inst. Hautes Études Sci. Publ. Math., 1988, 68, 211–221.
Berry M. V., Howls C. J. Stokes surfaces of difraction catastrophes with codimension three. Nonlinearity, 1990, 3(2), 281–291.
Kapranov M. M., Saito M. Hidden Stasheff polytopes in algebraic K-theory and in the space of Morse functions. In: Higher Homotopy Structures in Topology and Mathematical Physics. Proceedings of the International Conference held in honor of the 60th birthday of Jim Stasheff (Poughkeepsie, NY, 1996). Editor: J. McCleary. Providence, RI: Amer. Math. Soc., 1999, 191–225. (Contemp. Math., 227.)
Kostov V. P. On the stratification and singularities of the Stokes hypersurface of one-and two-parameter families of polynomials. In: Theory of Singularities and its Applications. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1990, 251–271. (Adv. Sov. Math., 1.)
Lando S. K. Geometry of the Stokes sets of families of functions of one variable. J. Math. Sci., 1997, 83(4), 534–538.
Wright F. J. The Stokes set of the cusp diffraction catastrophe. J. Phys. A, 1980, 13(9), 2913–2928.
1993-33 — M. B. Sevryuk
Arnold V. I.A-graded algebras and continued fractions. Comm. Pure Appl. Math., 1989, 42(7), 993–1000. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 473–482.]
Arnold V. I. Higher dimensional continued fractions. Reg. Chaot. Dynamics, 1998, 3(3), 10–17.
Arnold V. I. Continued Fractions. Moscow: Moscow Center for Continuous Mathematical Education Press, 2001 (in Russian). (“Mathematical Education” Library, 14.)
Kontsevich M. L., Sukhov Yu. M. Statistics of Klein polyhedra and multidimensional continued fractions. In: Pseudoperiodic Topology. Editors: V. Arnold, M. Kontsevich and A. Zorich. Providence, RI: Amer. Math. Soc, 1999, 9–27. (AMS Transl., Ser. 2, 197; Adv. Math. Sci., 46.)
1993-35
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1993-36
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1993-37
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1993-38
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1993-39
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1993-40
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1993-41
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1993-41 — M. R. Entov
Entov M. R. Surgery on Lagrangian and Legendrian singularities. Geom. Funct. Anal., 1999, 9(2), 298–352.
1993-42
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1993-43
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1993-44
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1993-45
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1993-46
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1993-47
Arnold V. I. Problems on singularities and dynamical systems. In: Developments in Mathematics: the Moscow School. Editors: V. I. Arnold and M. Monastyrsky. London: Chapman & Hall, 1993, 251–274.
1993-48 — M. B. Sevryuk
Montaldi J. Caustics in time reversible Hamiltonian systems. In: Singularity Theory and its Applications, Part II. Editors: M. Roberts and I. Stewart. Berlin: Springer, 1991, 266–277. (Lecture Notes in Math., 1463.)
Quispel G. R. W., Sevryuk M. B. KAM theorems for the product of two involutions of different types. Chaos, 1993, 3(4), 757–769.
1994-2 — S. L. Tabachnikov
Segre B. Alcune proprietà differenziali in grande delle curve chiuse sghembe. Rend. Mat., Ser. 6, 1968, 1, 237–297.
Weiner J. Global properties of spherical curves. J. Differ. Geom., 1977, 12(3), 425–434.
1994-5 — V. D. Sedykh
Anisov S. S. Convex curves in \(\mathbb{R}\)Pn. Proc. Steklov Inst. Math., 1998, 221, 3–39.
1994-6 — V. D. Sedykh
Arnold V. I. Towards the Legendre Sturm theory of space curves. Funct. Anal. Appl., 1998, 32(2), 75–80.
Sedykh V. D. Some invariants of admissible homotopies of space curves. Funct. Anal. Appl., 2001, 35(4), 284–293.
1994-6 — R. Uribe-Vargas
Arnold V. I. Towards the Legendre Sturm theory of space curves. Funct. Anal. Appl., 1998, 32(2), 75–80.
Uribe-Vargas R. Symplectic and contact singularities in the differential geometry of curves and surfaces. Ph. D. Thesis, Université Paris 7, 2001, Ch. 3, § 7.
1994-8 — S. L. Tabachnikov
Chmutov S. V., Goryunov V. V. Polynomial invariants of Legendrian links and plane fronts. In: Topics in Singularity Theory. V. I. Arnold's 60th Anniversary Collection. Editors: A. Khovanskiĭ, A. Varchenko and V. Vassiliev. Providence, RI: Amer. Math. Soc., 1997, 25–43. (AMS Transl., Ser. 2, 180; Adv. Math. Sci., 34.)
Chmutov S. V., Goryunov V. V, Murakami H. Regular Legendrian knots and the HOMFLY polynomial of immersed plane curves. Math. Ann., 2000, 317(3), 389–413.
Tabachnikov S. L. Estimates for the Bennequin number of Legendrian links from state models for knot polynomials. Math. Res. Lett., 1997, 4(1), 143–156.
Tabachnikov S. L., Fuchs D. B. Invariants of Legendrian and transverse knots in the standard contact space. Topology, 1997, 36(5), 1025–1053.
1994-10 — S. V. Duzhin
Gusein-Zade S. M., Duzhin F. S. On the number of topological types of plane curves. Russian Math. Surveys, 1998, 53(3), 626–627.
Jacobsen J. L., Zinn-Justin P. A transfer matrix approach to the enumeration of knots. [Internet: http://www.arXiv.org/abs/math-ph/0102015]
1994-10 — S. K. Lando
Arnold V. I. Plane curves, their invariants, perestroikas and classifications. In: Singularities and Bifurcations. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1994, 33–91. (Adv. Sov. Math., 21.)
Gusein-Zade S. M. On the enumeration of curves from infinity to infinity. In: Singularities and Bifurcations. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1994, 189–198. (Adv. Sov. Math., 21.)
Gusein-Zade S. M., Duzhin F. S. On the number of topological types of plane curves. Russian Math. Surveys, 1998, 53(3), 626–627.
Lando S. K. On enumeration of unicursal curves. In: Differential and Symplectic Topology of Knots and Curves. Editor: S. Tabachnikov. Providence, RI: Amer. Math. Soc., 1999, 77–81. (AMS Transl., Ser. 2, 190; Adv. Math. Sci., 42.)
1994-11 — V. I. Arnold
Arnold V. I. Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect. Selecta Math. (N. S.), 1995, 1(1), 1–19. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 583–604.]
1994-13 — V. L. Ginzburg
Ginzburg V. L. An embedding \(\mathbb{R}\), 2n − 1 ≥ 7, whose Hamiltonian flow has no periodic trajectories. Internat. Math. Res. Notices, 1995, 2, 83–97 (electronic).
Ginzburg V. L. A smooth counterexample to the Hamiltonian Seifert conjecture in \(\mathbb{R}\). Internat. Math. Res. Notices, 1997, 13, 641–650.
Ginzburg V. L. Hamiltonian dynamical systems without periodic orbits. In: Northern California Symplectic Geometry Seminar. Editors: Ya. Eliashberg, D. Fuchs, T. Ratiu and A. Weinstein. Providence, RI: Amer. Math. Soc., 1999, 35–48. (AMS Transl., Ser. 2, 196; Adv. Math. Sci., 45.)
Ginzburg V. L. The Hamiltonian Seifert conjecture: examples and open problems. In: European Congress of Mathematics (Barcelona, 2000), Vol. II. Editors: C. Casacuberta, R. M. Miró-Roig, J. Verdera and S. Xambó-Descamps. Basel: Birkhäuser, 2001, 547–555. (Progr. Math., 202.) [Internet: http://www.arXiv.org/abs/math.DG/0004020]
Ginzburg V. L., Gürel B. Z. On the construction of a C2-counterexample to the Hamiltonian Seifert Conjecture in \(\mathbb{R}\). [Internet: http://www.arXiv.org/abs/math.DG/0109153]
Ginzburg V. L., Gürel B. Z. A C2-smooth counterexample to the Hamiltonian Seifert Conjecture in \(\mathbb{R}\). Electron. Res. Announc. Amer. Math. Soc., 2002, 8, 11–19 (electronic). [Internet: http://www.arXiv.org/abs/math.DG/0110047]
Harrison J.C2 counterexamples to the Seifert conjecture. Topology, 1988, 27(3), 249–278.
Herman M.-R. Examples of compact hypersurfaces in \(\mathbb{R}\)2p, 2p ≥ 6, with no periodic orbits. In: Hamiltonian Systems with Three or More Degrees of Freedom (S'Agaró, 1995). Editor: C. Simó. Dordrecht: Kluwer Acad. Publ., 1999, 126. (NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 533.)
Kerman E. New smooth counterexamples to the Hamiltonian Seifert conjecture. J. Symplectic Geom., 2002, 1(2), 253–267. [Internet: http://www.arXiv.org/abs/math.DG/0101185]
Kuperberg G. A volume-preserving counterexample to the Seifert conjecture. Comment. Math. Helvetici, 1996, 71(1), 70–97.
Kuperberg G., Kuperberg K. Generalized counterexamples to the Seifert conjecture. Ann. Math., Ser. 2, 1996, 143(3), 547–576; 144(2), 239–268.
Kuperberg K. A smooth counterexample to the Seifert conjecture in dimension three. Ann. Math., Ser. 2, 1994, 140(3), 723–732.
Kuperberg K. Counterexamples to the Seifert conjecture. In: Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998). Doc. Math., 1998, Extra Vol. (II), 831–840 (electronic).
Kuperberg K. Aperiodic dynamical systems. Notices Amer. Math. Soc., 1999, 46(9), 1035–1040.
Schweitzer P. A. Counterexamples to the Seifert conjecture and opening closed leaves of foliations. Ann. Math., Ser. 2, 1974, 100, 386–400.
Seifert H. Closed integral curves in the 3-space and isotopic two-dimensional deformations. Proc. Amer. Math. Soc., 1950, 1, 287–302.
Wilson F. W., Jr. On the minimal sets of non-singular vector fields. Ann. Math., Ser. 2, 1966, 84(3), 529–536.
1994-15 — V. D. Sedykh
Shapiro M. Z. Topology of the space of non-degenerate curves. Izv. Math., 1994, 43(2), 291–310.
Anisov S. S. Convex curves in \(\mathbb{R}\)Pn. Proc. Steklov Inst. Math., 1998, 221, 3–39.
1994-15 — B. Z. Shapiro
Anisov S. S. Convex curves in \(\mathbb{R}\)Pn. Proc. Steklov Inst. Math., 1998, 221, 3–39.
Shapiro B. Z. Spaces of linear differential equations, and flag manifolds. Math. USSR, Izv., 1991, 36(1), 183–197.
1994-15 — R. Uribe-Vargas
Anisov S. S. Convex curves in \(\mathbb{R}\)Pn. Proc. Steklov Inst. Math., 1998, 221, 3–39.
Uribe-Vargas R. Symplectic and contact singularities in the differential geometry of curves and surfaces. Ph. D. Thesis, Université Paris 7, 2001, Ch. 3, § 5.
1994-16 — B. A. Khesin
Ovsienko V. Yu., Khesin B. A. Symplectic leaves of the Gelfand-Dikiĭ brackets and homotopy classes of nondegenerate curves. Funct. Anal. Appl., 1990, 24(1), 33–40.
1994-17 — B. Z. Shapiro
Sedykh V. D., Shapiro B. Z. On Young hulls of convex curves in \(\mathbb{R}\)>J. Geometry, 1998, 63(1–2), 168–182.
1994-17 — S. L. Tabachnikov
Wilczyński E. Projective Differential Geometry of Curves and Ruled Surfaces. Leipzig: B. G. Teubner, 1906; reprinted by Chelsea: New York, 1962.
1994-20 — F. Aicardi
Joets A., Ribotta R. Caustique de la surface ellipsoîdale â trois dimensions. Experim. Math., 1999, 8(1), 49–55.
1994-21 — S. V. Chmutov, E. Ferrand
Chmutov S. V., Goryunov V. V., Murakami H. Regular Legendrian knots and the HOMFLY polynomial of immersed plane curves. Math. Ann., 2000, 317(3), 389–413.
Ferrand E. Singularities cancellation on wave fronts. Topology Appl., 1999, 95(2), 155–163.
1994-22 — V. D. Sedykh
Anisov S. S. Projective convex curves. In: The Arnold-Gelfand Mathematical Seminars: Geometry and Singularity Theory. Editors: V. I. Arnold, I. M. Gelfand, V. S. Retakh and M. Smirnov. Boston, MA: Birkhäuser, 1997, 93–99.
1994-23 — B. Z. Shapiro
Shapiro B. Z. Discriminants of convex curves are homeomorphic. Proc. Amer. Math. Soc., 1998, 126(7), 1923–1930.
Shapiro B. Z., Shapiro M. Z. Projective convexity in \(\mathbb{R}\) implies Grassmann convexity. Internat. J. Math., 2000, 11(4), 579–588.
1994-24
Arnold V. I. Mathematical problems in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math. Sci., 100.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.
1994-25
Arnold V. I. Mathematical problems in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math. Sci., 100.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.
1994-26
Arnold V. I. Mathematical problems in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math. Sci., 100.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.
1994-27
Arnold V. I. Mathematical problems in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math. Sci., 100.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.
1994-28
Arnold V. I. Mathematical problems in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math. Sci., 100.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.
1994-29
Arnold V. I. Mathematical problems in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math. Sci., 100.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.
1994-30
Arnold V. I. Mathematical problems in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math. Sci., 100.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.
1994-31
Arnold V. I. Mathematical problems in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math. Sci., 100.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.
1994-32
Arnold V. I. Mathematical problems in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math. Sci., 100.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.
1994-33
Arnold V. I. Mathematical problems in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math. Sci., 100.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.
1994-34
Arnold V. I. Mathematical problems in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math. Sci., 100.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.
1994-35
Arnold V. I. Mathematical problems in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math. Sci., 100.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.
1994-36
Arnold V. I. Mathematical problems in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math. Sci., 100.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.
1994-37
Arnold V. I. Mathematical problems in classical physics. In: Trends and Perspectives in Applied Mathematics. Editors: F. John, J. E. Marsden and L. Sirovich. New York: Springer, 1994, 1–20. (Appl. Math. Sci., 100.)
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 553–575.
1994-38
Arnold V. I. Problèmes résolubles et problèmes irrésolubles analytiques et géométriques. In: Passion des Formes. Dynamique Qualitative Sémiophysique et Intelligibilité Dédié à R. Thom. Fontenay-St Cloud: ENS Éditions, 1994, 411–417; In: Formes et Dynamique, Renaissance d'un Paradigme. Hommage à René Thom. Paris: Eshel, 1995.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 577–582.
Arnold V. I. Sur quelques problèmes de la théorie des systèmes dynamiques. Topol. Methods Nonlinear Anal., 1994, 4(2), 209–225.
The Russian translation in: [2b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 533–551.
1994-39
Arnold V. I. Problèmes résolubles et problèmes irrésolubles analytiques et géométriques. In: Passion des Formes. Dynamique Qualitative Sémiophysique et Intelligibilité. Dédié à R. Thom. Fontenay-St Cloud: ENS Éditions, 1994, 411–417; In: Formes et Dynamique, Renaissance d'un Paradigme. Hommage à René Thom. Paris: Eshel, 1995.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 577–582.
1994-40
Arnold V. I. Problèmes résolubles et problèmes irrésolubles analytiques et géométriques. In: Passion des Formes. Dynamique Qualitative Sémiophysique et Intelligibilité. Dédié à R. Thom. Fontenay-St Cloud: ENS Éditions, 1994, 411–417; In: Formes et Dynamique, Renaissance d'un Paradigme. Hommage à René Thom. Paris: Eshel, 1995.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 577–582.
1994-41
Arnold V. I. Problèmes résolubles et problèmes irrésolubles analytiques et géométriques. In: Passion des Formes. Dynamique Qualitative Sémiophysique et Intelligibilité. Dédié à R. Thom. Fontenay-St Cloud: ENS Éditions, 1994, 411–417; In: Formes et Dynamique, Renaissance d'un Paradigme. Hommage à René Thom. Paris: Eshel, 1995.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 577–582.
Arnold V. I. Sur quelques problèmes de la théorie des systèmes dynamiques. Topol. Methods Nonlinear Anal., 1994, 4(2), 209–225.
The Russian translation in: [2b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 533–551.
1994-42
Arnold V. I. Problèmes résolubles et problèmes irrésolubles analytiques et géométriques. In: Passion des Formes. Dynamique Qualitative Sémiophysique et Intelligibilité. Dédié à R. Thom. Fontenay-St Cloud: ENS Éditions, 1994, 411–417; In: Formes et Dynamique, Renaissance d'un Paradigme. Hommage à René Thom. Paris: Eshel, 1995.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 577–582.
1994-43
Arnold V. I. Sur quelques problèmes de la théorie des systèmes dynamiques. Topol. Methods Nonlinear Anal., 1994, 4(2), 209–225.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 533–551.
1994-44
Arnold V. I. Sur quelques problèmes de la théorie des systèmes dynamiques. Topol. Methods Nonlinear Anal., 1994, 4(2), 209–225.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 533–551.
1994-45
Arnold V. I. Sur quelques problèmes de la théorie des systèmes dynamiques. Topol. Methods Nonlinear Anal., 1994, 4(2), 209–225.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 533–551.
1994-46
Arnold V. I. Sur quelques problèmes de la théorie des systèmes dynamiques. Topol. Methods Nonlinear Anal., 1994, 4(2), 209–225.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 533–551.
1994-47
Arnold V. I. Sur quelques problèmes de la théorie des systèmes dynamiques. Topol. Methods Nonlinear Anal., 1994, 4(2), 209–225.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 533–551.
1994-48
Arnold V. I. Sur quelques problèmes de la théorie des systèmes dynamiques. Topol. Methods Nonlinear Anal., 1994, 4(2), 209–225.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 533–551.
1994-49
Arnold V. I. Sur quelques problèmes de la théorie des systèmes dynamiques. Topol. Methods Nonlinear Anal., 1994, 4(2), 209–225.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 533–551.
1994-50
Arnold V. I. Sur quelques problèmes de la théorie des systèmes dynamiques. Topol. Methods Nonlinear Anal., 1994, 4(2), 209–225.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 533–551.
1994-51
Arnold V. I. Sur quelques problèmes de la théorie des systèmes dynamiques. Topol. Methods Nonlinear Anal., 1994, 4(2), 209–225.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 533–551.
1994-52
Arnold V. I. Sur quelques problèmes de la théorie des systèmes dynamiques. Topol. Methods Nonlinear Anal., 1994, 4(2), 209–225.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 533–551.
1994-53
Arnold V. I. Sur quelques problèmes de la théorie des systèmes dynamiques. Topol. Methods Nonlinear Anal., 1994, 4(2), 209–225.
The Russian translation in: [1b] Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 533–551.
1995-1 — B. Z. Shapiro
Arnold V. I. Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges. Funct. Anal. Appl., 1996, 30(1), 1–14.
Arnold V. I. Topological classification of real trigonometric polynomials and cyclic serpents polyhedron. In: The Arnold-Gelfand Mathematical Seminars: Geometry and Singularity Theory. Editors: V. I. Arnold, I. M. Gelfand, V. S. Retakh and M. Smirnov. Boston, MA: Birkhäuser, 1997, 101–106. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 619–625.]
Shapiro B. Z. On the number of components of the space of trigonometric polynomials of degree n with 2n different critical values. Math. Notes, 1997, 62(4), 529–534.
Shapiro B. Z., Vainshtein A. D. On the number of connected components in the space of M-polynomials in hyperbolic functions. Adv. Appl. Math., to appear.
1995-3 — F. Aicardi
Aicardi F. Letter to D. Panov, November 1997.
Arnold V. I. Topological problems in wave propagation theory and topological economy principle in algebraic geometry. In: The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (Toronto, 1997). Editors: E. Bierstone, B. A. Khesin, A. G. Khovanskiĭ and J. E. Marsden. Providence, RI: Amer. Math. Soc, 1999, 39–54. (Fields Inst. Commun., 24.)
Panov D. A. Parabolic curves and gradient mappings. Proc. Steklov Inst. Math., 1998, 221, 261–278.
1995-9 — F. Aicardi
Chekanov Yu. V., Pushkar' P. E. The combinatorics of fronts of Legendrian knots. Arnold's conjecture and invariants of Legendrian knots. Preprint (in Russian).
Etnyre J. B., Honda K. Knots and contact geometry. [Internet: http://www.arXiv.org/abs/math.DG/0006112]
Ferrand E. Families génératrices et nœuds legendriens. Thèse, École Polytechnique, 1997, Chapitre II, section 4.2.6.
Fraser M. Example of nonisotopic Legendrian curves not distinguished by the invariants tb and r. Internat. Math. Res. Notices, 1996, 19, 923–928.
Lenny Ny L. Computable Legendrian invariants. Preprint, 2000.
Traynor L. Legendrian circular helix links. Math. Proc. Cambridge Phil. Soc., 1997, 122(2), 301–314.
1995-10 — E. Ferrand
Entov M. R. On the necessity of Legendrian fold singularities. Internat. Math. Res. Notices, 1998, 20, 1055–1077.
Ferrand E., Pushkar' P. E. Non-cancellation of cusps on wave fronts. C. R. Acad. Sci. Paris, Sér. I Math., 1998, 327(9), 827–831.
1995-10 — F. Aicardi
Ferrand E., Pushkar' P. E. Non-cancellation of singularities on wave fronts. Preprint, CEREMADE 9842, Université Paris-Dauphine, 1998.
1995-11 — B. Z. Shapiro
Shapiro B. Z. Tree-like curves and their number of inflection points. In: Differential and Symplectic Topology of Knots and Curves. Editor: S. Tabachnikov. Providence, RI: Amer. Math. Soc., 1999, 113–129. (AMS Transl., Ser. 2, 190; Adv. Math. Sci., 42.)
1995-13 — V. M. Zakalyukin
Arnold V. I. Topological Invariants of Plane Curves and Caustics. Dean Jacqueline B. Lewis Memorial Lectures, Rutgers University. Providence, RI: Amer. Math. Soc., 1994. (University Lecture Series, 5.)
Kazarian M. E. Umbilical characteristic numbers of Lagrangian mappings of 3-dimensional pseudo-optical manifolds. In: Singularities and Differential Equations (Warsaw, 1993). Editors: S. Janeczko, W. M. Zajączkowski and B. Ziemian. Warsaw: Polish Academy of Sciences, Institute of Mathematics, 1996, 161–170. (Banach Center Publ., 33.)
Zakalyukin V. M. Maxwell stratum of Lagrangian collapse. Proc. Steklov Inst. Math., 1998, 221, 187–201.
1996-2 — V. A. Vassiliev
Arnold V. I. Plane curves, their invariants, perestroikas and classifications. In: Singularities and Bifurcations. Editor: V. I. Arnold. Providence, RI: Amer. Math. Soc., 1994, 33–91. (Adv. Sov. Math., 21.)
Vassiliev V. A. Complexes of connected graphs. In: The Gelfand Mathematical Seminars 1990–1992. Editors: L. Corwin, I. Gelfand and J. Lepowsky. Boston, MA-Basel: Birkhäuser, 1993, 223–235.
Vassiliev V. A. On finite order invariants of triple point free plane curves. In: Differential Topology, Infinite-Dimensional Lie Algebras, and Applications. D. B. Fuchs’ 60th Anniversary Collection. Editors: A. Astashkevich and S. Tabachnikov. Providence, RI: Amer. Math. Soc., 1999, 275–300. (AMS Transl., Ser. 2, 194; Adv. Math. Sci., 44.)
1996-3 — S. V. Duzhin, Ya. G. Mostovoy
Arnold V. I. Topological content of the Maxwell theorem on multipole representation of spherical functions. Topol. Methods Nonlinear Anal., 1996, 7(2), 205–217.
Arnold V. I. Lectures on Partial Differential Equations, 2nd supplemented edition. Moscow: PHASIS, 1997 (in Russian).
Dupont J. L., Lusztig G. On manifolds satisfying w 21 = 0. Topology, 1971, 10, 81–92.
1996-5 — A. E. Eremenko, D. I. Novikov
Eremenko A. E., Novikov D. I. Oscillation of Fourier integrals with a spectral gap. [Internet: http://www.arXiv.org/abs/math.CA/0301060]
1996-5 — S. B. Kuksin
Courant R., Hilbert D. Methods of Mathematical Physics, Vol. I. New York: Wiley Interscience, 1953; reprinted 1989. [The German original 1943.]
Cramér H., Leadbetter M. R. Stationary and Related Stochastic Processes. Sample Function Properties and their Applications. New York-London-Sydney: John Wiley, 1967.
Gantmacher F. R., KreĬn M. G. Oscillating Matrices and Small Oscillations of Mechanical Systems Moscow-Leningrad: OGIZ, 1941 (in Russian). [The German translation: Oscillationsmatrizen, Oscillationskerne und kleine Schwingungen mechanischer Systeme. Berlin: Akademie Verlag, 1960.]
Hartman P. Ordinary Differential Equations. New York-London-Sydney: John Wiley, 1964.
Hurwitz A. Über die Fourierschen Konstanten integrierbarer Funktionen. Math. Ann., 1903, 57(4), 425–446.
Ince E. L. Ordinary Differential Equations. New York: Dover, 1944.
Levin B. Ya. Distribution of Zeros of Entire Functions. Providence, RI: Amer. Math. Soc., 1964. [The Russian original 1956.]
Sturm J. C. F. Mémoire sur les équations différentielles du second ordre. J. Math. Pures Appl., 1836, 1, 106–186.
Tabachnikov S. L. Around four vertices. Russian Math. Surveys, 1990, 45(1), 229–230.
1996-6 — F. Aicardi
Arnold V. I. Topological Invariants of Plane Curves and Caustics. Dean Jacqueline B. Lewis Memorial Lectures, Rutgers University. Providence, RI: Amer. Math. Soc., 1994. (University Lecture Series, 5.)
Arnold V. I. Invariants and perestroikas of plane fronts. Proc. Steklov Inst. Math., 1995, 209, 11–56.
Barner M., Flohr F. Der Vierscheitelsatz und seine Verallgemeinerung. Der Mathematikunterricht, 1958, 4, 43–73.
Darboux J. G. Leçons sur la théorie générale des surfaces, Vol. 1, 2e édition. Paris, 1914, § VII, 291–293.
1996-9 — V. D. Sedykh
Sedykh V. D. On some classes of curves in a projective space. In: Geometry and Topology of Caustics—CAUSTICS'98 (Warsaw). Editors: S. Janeczko and V. M. Zakalyukin. Warsaw: Polish Academy of Sciences, Institute of Mathematics, 1999, 237–266. (Banach Center Publ., 50.)
1996-14 — M. L. Kontsevich
Eliashberg Ya. M. Invariants in contact topology. In: Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998). Doc. Math., 1998, Extra Vol. II, 327–338 (electronic).
1996-15 — V. I. Arnold
Arnold V. I. Arithmetics of Binary Quadratic Forms, Symmetry of Their Continued Fractions, and Geometry of Their de Sitter World. Moscow: Moscow Center for Continuous Mathematical Education Press, 2002.
1996-20 — M. B. Sevryuk
Broer H. W., Huitema G. B., Sevryuk M. B. Quasi-Periodic Motions in Families of Dynamical Systems: Order amidst Chaos. Berlin: Springer, 1996. (Lecture Notes in Math., 1645.)
Herman M. R. Existence et non existence de tores invariants par des difféomorphismes symplectiques. Palaiseau: École Polytech., Centre de Math., 1988. (Séminaire sur les Équations aux Dérivées Partielles 1987–1988, Exp. № 14.)
Herman M. R. Inégalités “a priori” pour des tores lagrangiens invariants par des difféomorphismes symplectiques. Inst. Hautes Études Sci. Publ. Math., 1989, 70, 47–101.
Quispel G. R. W., Sevryuk M. B. KAM theorems for the product of two involutions of different types. Chaos, 1993, 3(4), 757–769.
1997-6 — F. Aicardi
Aicardi F. Letter to D. Panov, November 1997.
1997-8 — Yu. M. Baryshnikov, M. Garay
Garay M. The classical and Legendrian theory of vanishing flattening points of plane and spatial curves. Ph. D. Thesis, Université Paris 7, 2001.
Uribe-Vargas R. On vanishing vertices at a Morse critical point. Talk at V. I. Arnold's seminar, 1995.
1997-8 — R. Uribe-Vargas
Agrachev A. A., Charlot G., Gauthier J. P., Zakalyukin V. M. On stability of generic sub-Riemannian caustics in the three-space. C. R. Acad. Sci. Paris, Sér. I Math., 2000, 330(6), 465–470.
Uribe-Vargas R. Symplectic and contact singularities in the differential geometry of curves and surfaces. Ph. D. Thesis, Université Paris 7, 2001, Ch. 6.
1997-9 — V. I. Arnold
Arnold V. I. Modes and quasimodes. Funct. Anal. Appl., 1972, 6(2), 94–101. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 189–202.]
Arnold V. I. Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect. Selecta Math. (N. S.), 1995, 1(1), 1–19. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 583–604.]
Frenkel I. B., Turaev V. G. Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions. In: The Arnold-Gelfand Mathematical Seminars: Geometry and Singularity Theory. Editors: V. I. Arnold, I. M. Gelfand, V. S. Retakh and M. Smirnov. Boston, MA: Birkhäuser, 1997, 171–204.
1997-9 — B. A. Khesin
Donaldson S. K., Thomas R. P. Gauge theory in higher dimensions. In: The Geometric Universe. Science, Geometry, and the Work of Roger Penrose. Papers from Symp. on geometric issues in the foundations of science held in honor of the 65th birthday of Sir Roger Penrose (Oxford, June 1996). Editors: S. A. Huggett, L. J. Mason, K. P. Tod, S. T. Tsou and N. M. J. Woodhouse. Oxford: Oxford University Press, 1998, 31–47.
Frenkel I. B., Khesin B. A. Four-dimensional realization of two-dimensional current groups. Commun. Math. Phys., 1996, 178(3), 541–562.
khesin B. A. Informal complexification and Poisson structures on moduli spaces. In: Topics in Singularity Theory. V. I. Arnold's 60th Anniversary Collection. Editors: A. Khovanskiĭ, A. Varchenko and V. Vassiliev. Providence, RI: Amer. Math. Soc., 1997, 147–155. (AMS Transl., Ser. 2, 180; Adv. Math. Sci., 34.)
khesin B. A., Rosly A. A. Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces. In: The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (Toronto, 1997). Editors: E. Bierstone, B. A. Khesin, A. G. Khovanskiĭ and J. E. Marsden. Providence, RI: Amer. Math. Soc., 1999, 311–323. (Fields Inst. Commun., 24.)
Khesin B. A., Rosly A. A. Polar homology and holomorphic bundles. Phil. Trans. Roy. Soc. London, Ser. A, 2001, 359, 1413–1427.
1998-2 — V. I. Arnold
Arnold V. I. Remarks on the parabolic curves on surfaces and on the higher-dimensional Möbius-Sturm theory. Funct. Anal. Appl., 1997, 31(4), 227–239.
Panov D. A. Parabolic curves and gradient mapping. Proc. Steklov Inst. Math., 1998, 221, 261–278.
Segre B. The Non-singular Cubic Surfaces. Oxford: Oxford University Press, 1942.
1998-3 — V. I. Arnold
Arnold V. I. Remarks on the parabolic curves on surfaces and on the higher-dimensional Möbius-Sturm theory. Funct. Anal. Appl., 1997, 31(4), 227–239.
1998-4 — V. I. Arnold
arnold V. I. Remarks on the parabolic curves on surfaces and on the higher-dimensional Möbius-Sturm theory. Funct. Anal. Appl., 1997, 31(4), 227–239.
1998-5 — V. I. Arnold
Arnold V. I. On the problem of realization of a given Gaussian curvature function. CEREMADE (UMR 7534), Université Paris-Dauphine, № 9809, 12/02/1998; Topol. Methods Nonlinear Anal., 1998, 11(2), 199–206. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
1998-6 — V. I. Arnold
Arnold V. I. Towards the Legendre Sturm theory of space curves. Funct. Anal. Appl., 1998, 32(2), 75–80.
1998-6 — V. D. Sedykh
Arnold V. I. Towards the Legendre Sturm theory of space curves. Funct. Anal. Appl., 1998, 32(2), 75–80.
Sedykh V. D. Some invariants of admissible homotopies of space curves. Funct. Anal. Appl., 2001, 35(4), 284–293.
1998-9 — V. I. Arnold
Arnold V. I. On some problems in singularity theory. In: Geometry and Analysis. Papers dedicated to the memory of V. K. Patodi. Bangalore: Indian Acad. Sci., 1980, 1–9. [Reprinted in: Proc. Indian Acad. Sci. Math. Sci., 1981, 90(1), 1–9.]
1998-10 — V. I. Arnold
Arnold V. I. Polymathematics: is mathematics a single science or a set of arts? In: Mathematics: Frontiers and Perspectives. Editors: V. I. Arnold, M. Atiyah, P. Lax and B. Mazur. Providence, RI: Amer. Math. Soc., 2000, 403–416; CEREMADE (UMR 7534), Université Paris-Dauphine, № 9911, 10/03/1999. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
1998-10 — B. A. Khesin
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
Khesin B. A., Rosly A. A. Polar homology and holomorphic bundles. Phil. Trans. Roy. Soc. London, Ser. A, 2001, 359, 1413–1427.
1998-10 — M. L. Kontsevich
Bott R., Taubes C. On the self-linking of knots. Topology and physics. J. Math. Phys., 1994, 35(10), 5247–5287.
1998-11 — A. M. Gabrielov
Arnold V. I., Vassiliev V. A., Goryunov V. V., Lyashko O. V. Singularities. I. Local and Global Theory. Berlin: Springer, 1993. (Encyclopædia Math. Sci., 6; Dynamical Systems, VI.) [The Russian original 1988.]
Gabrielov A. M., KhovanskiĬ A. G. Multiplicity of a Noetherian intersection. In: Geometry of Differential Equations. Editors: A. G. Khovanskiĭ, A. N. Varchenko and V. A. Vassiliev. Providence, RI: Amer. Math. Soc., 1998, 119–130. (AMS Transl., Ser. 2, 186; Adv. Math. Sci., 39.)
Gromov M. L. Partial Differential Relations. Berlin: Springer, 1986.
1998-12
Arnold V. I. Topological problems in the theory of asymptotic curves. Proc. Steklov Inst. Math., 1999, 225, 5–15. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
1998-13 — V. I. Arnold, B. A. Khesin
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
Serre D. Les invariants du premier ordre de l'équation d'Euler en dimension 3. C. R. Acad. Sci. Paris, Sér. A–B, 1979, 289(4), A267–A270.
Serre D. Les invariants du premier ordre de l'équation d'Euler en dimension trois. Physica D, 1984, 13(1–2), 105–136.
1998-15 — V. I. Arnold
Arnold V. I. Relatives of the quotient of the complex projective plane by complex conjugation. Proc. Steklov Inst. Math., 1999, 224, 46–56. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
Ilyushechkin N. V. The discriminant of the characteristic polynomial of a normal matrix. Math. Notes, 1992, 51(3), 230–235.
1998-15 — S. V. Duzhin
Duzhin S. V. A remark on Arnold's problem concerning quaternionic determinants. Research Announcements of Arnold's Seminar, 12 October 1998. [Internet: http://www.pdmi.ras.ru/~arnsem/papers/resann.html]
1998-15 — M. B. Sevryuk
Aslaksen H. Quaternionic determinants. Math. Intelligencer, 1996, 18(3), 57–65.
Gelfand I. M., Retakh V. S. The determinants of matrices over non-commutative rings. Funct. Anal. Appl., 1991, 25(2), 91–102.
Gelfand I. M., Retakh V. S. The theory of non-commutative determinants and characteristic functions of graphs. Funct. Anal. Appl., 1992, 26(4), 231–246.
Kazarian M. E. A remark on the eigenvectors and eigenvalues of hyper-Hermitian matrices. Preprint, 1998 (in Russian). [Internet: http://www.pdmi.ras.ru/~arnsem/papers/]
1998-16 — V. I. Arnold
Arnold V. I. Modes and quasimodes. Funct. Anal. Appl., 1972, 6(2), 94–101. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 189–202.]
Arnold V. I. Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect. Selecta Math. (N. S.), 1995, 1(1), 1–19. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 583–604.]
Arnold V. I. Mysterious Mathematical Trinities. Topological Economy Principle in Algebraic Geometry. Moscow: Moscow Center for Continuous Mathematical Education Press, 1997 (in Russian).
Arnold V. I. Relatives of the quotient of the complex projective plane by complex conjugation. Proc. Steklov Inst. Math., 1999, 224, 46–56. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
Arnold V. I. Symplectization, complexification and mathematical trinities. In: The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (Toronto, 1997). Editors: E. Bierstone, B. A. Khesin, A. G. Khovanskiĭ and J. E. Marsden. Providence, RI: Amer. Math. Soc., 1999, 23–37. (Fields Institute Commun., 24.); CEREMADE (UMR 7534), Université Paris-Dauphine, № 9815, 04/03/1998. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
Arnold V. I. Polymathematics: is mathematics a single science or a set of arts? In: Mathematics: Frontiers and Perspectives. Editors: V. I. Arnold, M. Atiyah, P. Lax and B. Mazur. Providence, RI: Amer. Math. Soc., 2000, 403–416; CEREMADE (UMR 7534), Université Paris-Dauphine, № 9911, 10/03/1999. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
Kazarian M. E. A remark on the eigenvectors and eigenvalues of hyper-Hermitian matrices. Preprint, 1998 (in Russian). [Internet: http://www.pdmi.ras.ru/~arnsem/papers/]
1998-17 — V. I. Arnold
Arnold V. I. Lectures on Partial Differential Equations, 2nd supplemented edition. Moscow: PHASIS, 1997 (in Russian).
1998-17 — B. A. Khesin
Banyaga A. The geometry surrounding the Arnold-Liouville theorem. In: Advances in Geometry. Boston, MA: Birkhäuser, 1999, 53–69. (Progr. Math., 172.)
Banyaga A., Molino P. Complete integrability in contact geometry. Preprint, 1996; book in preparation.
Yudovich V. I. Cosymmetry, degeneration of solutions of operator equations, and the onset of filtration convection. Math. Notes, 1991, 49(5–6), 540–545.
Yudovich V. I. Secondary cycle of equilibria in a system with cosymmetry, its creation by bifurcation and impossibility of symmetric treatment of it. Chaos, 1995, 5(2), 402–411.
Yudovich V. I. Cosymmetry and dynamical systems. In: Proceedings of the Third International Congress on Industrial and Applied Mathematics (Hamburg, July 1995). Editors: E. Kreuzer and O. Mahrenholtz. Z. Angew. Math. Mech., 1996, 76,suppl. 4, 556–559.
Yudovich V. I. The implicit function theorem for cosymmetric equations. Math. Notes, 1996, 60(2), 313–317.
1998-19 — V. I. Arnold
Arnold V. I. Higher dimensional continued fractions. Reg. Chaot. Dynamics, 1998, 3(3), 10–17.
1998-19 — N. P. Dolbilin
Banaszczyk W. Additive Subgroups of Topological Vector Spaces. Berlin: Springer, 1991. (Lecture Notes in Math., 1466.)
Gruber P. M. Geometry of numbers. In: Handbook of Convex Geometry, Vol. B. Editors: P. M. Gruber and J. M. Wills. Amsterdam: North-Holland, 1993, 739–763.
Lagarias J. C., Lenstra H. W., Jr., Schnorr C.-P. Korkin-Zolotarëv bases and successive minima of a lattice and its reciprocal lattice. Combinatorica, 1990, 10(4), 333–348.
Yudin V. A. Two extremal problems for trigonometric polynomials. Sb. Math., 1996, 187(11), 1721–1736.
1998-20 — V. I. Arnold
Arnold V. I. Simple singularities of curves. CEREMADE (UMR 7534), Université Paris-Dauphine, № 9906, 09/02/1999; Proc. Steklov Inst. Math., 1999, 226, 20–28. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
Arnold V. I. First steps of local contact algebra. CEREMADE (UMR 7534), Université Paris-Dauphine, № 9909, 10/02/1999; Canad. J. Math., 1999, 51(6), 1123–1134. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
Arnold V. I. First steps of local symplectic algebra. CEREMADE (UMR 7534), Université Paris-Dauphine, № 9902, 20/01/1999; In: Differential Topology, Infinite-Dimensional Lie Algebras, and Applications. D. B. Fuchs’ 60th Anniversary Collection. Editors: A. Astashkevich and S. Tabachnikov. Providence, RI: Amer. Math. Soc., 1999, 1–8. (AMS Transl., Ser. 2, 194; Adv. Math. Sci., 44.) [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
Bruce J. W., Gaffney T. J. Simple singularities of mappings (ℂ,0) → (ℂ2,0). J. London Math. Soc., Ser. 2, 1982, 26(3), 465–474.
Gibson C. G., Hobbs C. A. Simple singularities of space curves. Math. Proc. Cambridge Phil. Soc., 1993, 113(2), 297–310.
1998-21 — V. I. Arnold
Low R. J. Twistor linking and causal relations. Classical Quantum Gravity, 1990, 7(2), 177–187.
Low R. J. Twistor linking and causal relations in exterior Schwarzschild space. Classical Quantum Gravity, 1994, 11(2), 453–456.
1998-22 — V. I. Arnold
Hass J., Lagarias J. The number of Reidemeister moves needed for unknoting. In: ICM 1998, International Congress of Mathematicians. Abstracts of short communications and poster sessions. Berlin-Bielefeld: University of Bielefeld Press, 1998, 89.
1998-22 — J. C. Lagarias
Adams C., Brennan B. M., Greilsheimer D. L., Woo A. K. Stick numbers and composition of knots and links. J. Knot Theory Ramifications, 1997, 6, 149–161.
Avis D., ElGindy H. Triangulating point sets in space. Discr. & Comp. Geom., 1987, 2, 99–111.
Chazelle B. Convex partitions of polyhedra: a lower bound and worst case optimal algorithm. SIAM J. Comput., 1984, 13, 488–507.
Hass J., Lagarias J. C. The number of Reidemeister moves needed for unknotting. J. Amer. Math. Soc., 2001, 14, 399–428. [Internet: http://www.arXiv.org/abs/math.GT/9807012]
Hass J., Lagarias J. C. Affine isoperimetric inequalities for piecewise linear surfaces. [Internet: http://www.arXiv.org/abs/math.GT/0202179]
Hass J., Lagarias J. C., Pippenger N. The computational complexity of knot and link problems. J. Assoc. Comp. Mach., 1999, 46(2), 185–211. [Internet: http://www.arXiv.org/abs/math.GT/9807016]
Hass J., Lagarias J. C., Thurston W. P. Area inequalities for embedded disks bounding unknotted curves, in preparation.
1998-24 — S. V. Duzhin
Symmetries and Conservation Laws for Differential Equations of Mathematical Physics. Editors: I. S. Krasil'shchik and A. M. Vinogradov. Providence, RI: Amer. Math. Soc., 1999. (Transl. Math. Monographs, 182.) [The Russian original 1997.]
1999-8 — M. B. Sevryuk
Arnold V. I. Simple singularities of curves. Proc. Steklov Inst. Math., 1999, 226, 20–28; CEREMADE (UMR 7534), Université Paris-Dauphine, № 9906, 09/02/1999. [Internet: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html]
Arnold V. I. Weak asymptotics for the numbers of solutions of Diophantine problems. Funct. Anal. Appl., 1999, 33(4), 292–293.
Arnold V. I. Frequent representations. Moscow Math. J., 2003, 3(4), 14 pp.
Herzog J. Generators and relations of Abelian semigroups and semigroup rings. Manuscripta Math., 1970, 3(2), 175–193.
Kunz E. The value-semigroup of a one-dimensional Gorenstein ring. Proc. Amer. Math. Soc., 1970, 25(4), 748–751.
Sylvester J. J. Mathematical questions with their solutions. Educational Times, 1884, 41, 21.
2000-7 — V. I. Arnold
Krasilov V. A. Macroevolution and evolutionary synthesis. In: Evolution, Ecology, Biodiversity. Proceedings of a conference in memory of N. N. Vorontsov (1934–2000) held on December 26–27, 2000. Editor: E. A. Lyapunova. Moscow: Research Center for Education Preceding the High School, 2001, 27–47 (in Russian).
Malyshev L. I. The quantitative analysis of flora: spatial diversity, the level of specific richness, and representativity of sampling areas. Botanicheskiĭ Zh., 1975, 60(11), 1537–1550 (in Russian).
2000-8 — M. B. Sevryuk
Arnold V. I. Complexification of tetrahedron and pseudoprojective transformations. Funct. Anal. Appl., 2001, 35(4), 241–246.
Arnold V. I. Pseudoquaternion geometry. Funct. Anal. Appl., 2002, 36(1), 1–12.
2000-9 — M. B. Sevryuk
Arnold V. I. Topological Invariants of Plane Curves and Caustics. Dean Jacqueline B. Lewis Memorial Lectures, Rutgers University. Providence, RI: Amer. Math. Soc., 1994. (University Lecture Series, 5.)
Arnold V. I. Invariants and perestroikas of plane fronts. Proc. Steklov Inst. Math., 1995, 209, 11–56.
Arnold V. I. On the topological properties of Legendrian projections in contact geometry of wave fronts. St. Petersburg Math. J., 1995, 6(3), 439–452.
Arnold V. I. Sur les propriétés topologiques des projections lagrangiennes en géométrie symplectique des caustiques. CEREMADE (UMR 7534), Université Paris-Dauphine, № 9320, 14/06/1993; Rev. Mat. Univ. Complut. Madrid, 1995, 8(1), 109–119. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 525–532.]
Arnold V. I. The geometry of spherical curves and quaternion algebra. Russian Math. Surveys, 1995, 50(1), 1–68.
Arnold V. I. On the number of flattening points of space curves. In: Sinaĭ's Moscow Seminar on Dynamical Systems. Editors: L. A. Bunimovich, B. M. Gurevich and Ya. B. Pesin. Providence, RI: Amer. Math. Soc., 1996, 11–22. (AMS Transl., Ser. 2, 171; Adv. Math. Sci., 28.)
Arnold V. I. Topological problems in the theory of wave propagation. Russian Math. Surveys, 1996, 51(1), 1–47.
Arnold V. I. Remarks on parabolic curves on surfaces and on higher dimensional Möbius-Sturm theory. Funct. Anal. Appl., 1997, 31(4), 227–239.
Arnold V. I. Mysterious Mathematical Trinities. Topological Economy Principle in Algebraic Geometry. Moscow: Moscow Center for Continuous Mathematical Education Press, 1997 (in Russian).
Arnold V. I. Topological problems in wave propagation theory and topological economy principle in algebraic geometry. In: The Arnoldfest. Proceedings of a conference in honour of V. I. Arnold for his sixtieth birthday (Toronto, 1997). Editors: E. Bierstone, B. A. Khesin, A. G. Khovanskiĭ and J. E. Marsden. Providence, RI: Amer. Math. Soc., 1999, 39–54. (Fields Institute Commun., 24.)
Arnold V. I. Topologically necessary singularities on moving wavefronts and caustics. In: Hamiltonian Systems with Three or More Degrees of Freedom (S'Agaró, 1995). Editor: C. Simó. Dordrecht: Kluwer Acad. Publ., 1999, 11–12. (NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 533.)
Arnold V. I. Symplectic geometry and topology. J. Math. Phys., 2000, 41(6), 3307–3343.
Arnold V. I. Astroidal geometry of hypocycloids and the Hessian topology of hyperbolic polynomials. Russian Math. Surveys, 2001, 56(6), 1019–1083.
Arnold V. I. Astroidal Geometry of Hypocycloids and the Hessian Topology of Hyperbolic Polynomials. Moscow: Moscow Center for Continuous Mathematical Education Press, 2001 (in Russian).
Arnold V. I. Wave Fronts and Topology of Curves. Moscow: PHASIS, 2002 (in Russian). (Young Mathematician's Library, 9.)
Blaschke W. Kreis und Kugel. Leipzig: Veit, 1916. [2te Auflage: Berlin: Walter de Gruyter, 1956.]
Hurwitz A. Über die Fourierschen Konstanten integrierbarer Funktionen. Math. Ann., 1903, 57(4), 425–446.
Kellogg O. D. The oscillation of functions of an orthogonal set. Amer. J. Math., 1916, 38(1), 1–5.
Natanzon S. M. Trigonometric tensors on algebraic curves of arbitrary genus. An analogue of the Sturm-Hurwitz theorem. Russian Math. Surveys, 1995, 50(6), 1286–1287.
Natanzon S. M. Moduli of real algebraic curves and their superanalogues. Spinors and Jacobians of real curves. Russian Math. Surveys, 1999, 54(6), 1091–1147.
Sturm J. C. F. Mémoire sur les équations différentielles du second ordre. J. Math. Pures Appl., 1836, 1, 106–186.
Tabachnikov S. L. Around four vertices. Russian Math. Surveys, 1990, 45(1), 229–230.
2000-10 — M. B. Sevryuk
Arnold V. I. Convex hulls and the increase of efficiency of systems under pulsating loading. Sib. Math. J., 1987, 28(4), 540–542.
Arnold V. I. Optimization in mean and phase transitions in controlled dynamical systems. Funct. Anal. Appl., 2002, 36(2), 83–92.
2000-11
Arnold V. I. On a variational problem connected with phase transitions of means in controllable dynamical systems. In: Nonlinear Problems in Mathematical Physics and Related Topics I. In honour of Professor O. A. Ladyzhenskaya. Editors: M. Sh. Birman, S. Hildebrandt, V. A. Solonnikov and N. N. Ural'tseva. Dordrecht: Kluwer Acad. Publ., 2002, 23–34. (Internat Math. Ser., 1.)
2000-12 — V. I. Arnold
Schütt C., Werner E. Random polytopes with vertices on the boundary of a convex body. C. R. Acad. Sci. Paris, Sér. I Math., 2000, 331(9), 697–701.
2000-12 — M. B. Sevryuk
Arnold V. I. A-graded algebras and continued fractions. Comm. Pure Appl. Math., 1989, 42(7), 993–1000. [The Russian translation in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 473–482.]
Arnold V. I. Higher dimensional continued fractions. Reg. Chaot. Dynamics, 1998, 3(3), 10–17.
Arnold V. I. Continued Fractions. Moscow: Moscow Center for Continuous Mathematical Education Press, 2001 (in Russian). (“Mathematical Education” Library, 14.)
Kontsevich M. L., Sukhov Yu. M. Statistics of Klein polyhedra and multidimensional continued fractions. In: Pseudoperiodic Topology. Editors: V. Arnold, M. Kontsevich and A. Zorich. Providence, RI: Amer. Math. Soc., 1999, 9–27. (AMS Transl., Ser. 2, 197; Adv. Math. Sci., 46.)
Korkina E. I. La périodicité des fractions continues multidimensionnelles. C. R. Acad. Sci. Paris, Sér. I Math., 1994, 319(8), 777–780.
Korkina E. I. Two-dimensional continued fractions. The simplest examples. Proc. Steklov Inst. Math., 1995, 209, 124–144.
Tsuchihashi H. 2-dimensional periodic continued fractions and 3-dimensional cusp singularities. Proc. Jap. Acad., Ser. A Math. Sci., 1982, 58(6), 262–264.
Tsuchihashi H. Higher-dimensional analogues of periodic continued fractions and cusp singularities. Tôhoku Math. J., Ser. 2, 1983, 35(4), 607–639.
2001-1
Arnold V. I. Astroidal geometry of hypocycloids and the Hessian topology of hyperbolic polynomials. Russian Math. Surveys, 2001, 56(6), 1019–1083.
Arnold V. I. Astroidal Geometry of Hypocycloids and the Hessian Topology of Hyperbolic Polynomials. Moscow: Moscow Center for Continuous Mathematical Education Press, 2001 (in Russian).
2001-2
Arnold V. I. Astroidal geometry of hypocycloids and the Hessian topology of hyperbolic polynomials. Russian Math. Surveys, 2001, 56(6), 1019–1083.
Arnold V. I. Astroidal Geometry of Hypocycloids and the Hessian Topology of Hyperbolic Polynomials. Moscow: Moscow Center for Continuous Mathematical Education Press, 2001 (in Russian).
2001-4 — V. I. Arnold
Arnold V. I. Topological Invariants of Plane Curves and Caustics. Dean Jacqueline B. Lewis Memorial Lectures, Rutgers University. Providence, RI: Amer. Math. Soc., 1994. (University Lecture Series, 5.)
Arnold V. I. Topological problems in the theory of wave propagation. Russian Math. Surveys, 1996, 51(1), 1–47.
2001-6
Arnold V. I. Astroidal geometry of hypocycloids and the Hessian topology of hyperbolic polynomials. Russian Math. Surveys, 2001, 56(6), 1019–1083.
Arnold V. I. Astroidal Geometry of Hypocycloids and the Hessian Topology of Hyperbolic Polynomials. Moscow: Moscow Center for Continuous Mathematical Education Press, 2001 (in Russian).
2002-1
Arnold V. I. Problems to the Seminar: 15 January 2002. CEREMADE (UMR 7534), Université Paris-Dauphine, № 0216, 16/05/2002.
Arnold V. I. What Is Mathematics? Moscow: Moscow Center for Continuous Mathematical Education Press, 2002, 104 pp.
2002-1 — V. I. Arnold
Arnold V. I. Astroidal geometry of hypocycloids and the Hessian topology of hyperbolic polynomials. Russian Math. Surveys, 2001, 56(6), 1019–1083.
Arnold V. I. Astroidal Geometry of Hypocycloids and the Hessian Topology of Hyperbolic Polynomials. Moscow: Moscow Center for Continuous Mathematical Education Press, 2001 (in Russian).
2002-2
Arnold V. I. Problems to the Seminar: 15 January 2002. CEREMADE (UMR 7534), Université Paris-Dauphine, № 0216, 16/05/2002.
Arnold V. I. What Is Mathematics? Moscow: Moscow Center for Continuous Mathematical Education Press, 2002, 104 pp.
2002-3
Arnold V. I. Problems to the Seminar: 15 January 2002. CEREMADE (UMR 7534), Université Paris-Dauphine, № 0216, 16/05/2002.
Arnold V. I. What Is Mathematics? Moscow: Moscow Center for Continuous Mathematical Education Press, 2002, 104 pp.
2002-4
Arnold V. I. Problems to the Seminar: 15 January 2002. CEREMADE (UMR 7534), Université Paris-Dauphine, № 0216, 16/05/2002.
Arnold V. I. What Is Mathematics? Moscow: Moscow Center for Continuous Mathematical Education Press, 2002, 104 pp.
2002-5
Arnold V. I. Problems to the Seminar: 15 January 2002. CEREMADE (UMR 7534), Université Paris-Dauphine, № 0216, 16/05/2002.
Arnold V. I. What Is Mathematics? Moscow: Moscow Center for Continuous Mathematical Education Press, 2002, 104 pp.
2002-6
Arnold V. I. Problems to the Seminar: 15 January 2002. CEREMADE (UMR 7534), Université Paris-Dauphine, № 0216, 16/05/2002.
Arnold V. I. What Is Mathematics? Moscow: Moscow Center for Continuous Mathematical Education Press, 2002, 104 pp.
2002-7
Arnold V. I. Problems to the Seminar: 15 January 2002. CEREMADE (UMR 7534), Université Paris-Dauphine, № 0216, 16/05/2002.
Arnold V. I. What Is Mathematics? Moscow: Moscow Center for Continuous Mathematical Education Press, 2002, 104 pp.
2002-7 — V. I. Arnold
Arnold V. I. The asymptotic Hopf invariant and its applications. In: Proceedings of the All-Union School on Differential Equations with Infinitely Many Independent Variables and on Dynamical Systems with Infinitely Many Degrees of Freedom (Dilizhan, May 21–June 3, 1973). Yerevan: AS of Armenian SSR, 1974, 229–256 (in Russian). [The English translation: Selecta Math. Sov., 1986, 5(4), 327–345.] [The Russian original is reprinted and supplemented in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 215–236.]
Arnold V. I., Khesin B. A. Topological Methods in Hydrodynamics. New York: Springer, 1998. (Appl. Math. Sci., 125.)
2002-8
Arnold V. I. Problems to the Seminar: 15 January 2002. CEREMADE (UMR 7534), Université Paris-Dauphine, № 0216, 16/05/2002.
Arnold V. I. What Is Mathematics? Moscow: Moscow Center for Continuous Mathematical Education Press, 2002, 104 pp.
2002-8 — V. I. Arnold
Arnold V. I. Small denominators and problems of stability of motion in classical and celestial mechanics. Russian Math. Surveys, 1963, 18(6), 85–191.
Zorich A. How do the leaves of a closed 1-form wind around a surface? In: Pseudoperiodic Topology. Editors: V. Arnold, M. Kontsevich and A. Zorich. Providence, RI: Amer. Math. Soc., 1999, 135–178. (AMS Transl., Ser.2, 197; Adv. Math. Sci., 46.)
2002-9
Arnold V. I. Problems to the Seminar: 15 January 2002. CEREMADE (UMR 7534), Université Paris-Dauphine, № 0216, 16/05/2002.
Arnold V. I. What Is Mathematics? Moscow: Moscow Center for Continuous Mathematical Education Press, 2002, 104 pp.
2002-9 — V. I. Arnold
Arnold V. I. Complexification of tetrahedron and pseudoprojective transformations. Funct. Anal. Appl., 2001, 35(4), 241–246.
Arnold V. I. Pseudoquaternion geometry. Funct. Anal. Appl., 2002, 36(1), 1–12.
2002-10
Arnold V. I. Problems to the Seminar: 15 January 2002. CEREMADE (UMR 7534), Université Paris-Dauphine, № 0216, 16/05/2002.
Arnold V. I. What Is Mathematics? Moscow: Moscow Center for Continuous Mathematical Education Press, 2002, 104 pp.
2002-11
Arnold V. I. Problems to the Seminar: 15 January 2002. CEREMADE (UMR 7534), Université Paris-Dauphine, № 0216, 16/05/2002.
Arnold V. I. What Is Mathematics? Moscow: Moscow Center for Continuous Mathematical Education Press, 2002, 104 pp.
2002-12
Arnold V. I. Problems to the Seminar: 15 January 2002. CEREMADE (UMR 7534), Université Paris-Dauphine, № 0216, 16/05/2002.
Arnold V. I. What Is Mathematics? Moscow: Moscow Center for Continuous Mathematical Education Press, 2002, 104 pp.
2002-12 — V. I. Arnold
Arnold V. I. Topological Invariants of Plane Curves and Caustics. Dean Jacqueline B. Lewis Memorial Lectures, Rutgers University. Providence, RI: Amer. Math. Soc., 1994. (University Lecture Series, 5.)
2002-13
Arnold V. I. Problems to the Seminar: 15 January 2002. CEREMADE (UMR 7534), Université Paris-Dauphine, № 0216, 16/05/2002.
Arnold V. I. What Is Mathematics? Moscow: Moscow Center for Continuous Mathematical Education Press, 2002, 104 pp.
2002-13 — V. I. Arnold
Arnold V. I. Astroidal geometry of hypocycloids and the Hessian topology of hyperbolic polynomials. Russian Math. Surveys, 2001, 56(6), 1019–1083.
Arnold V. I. Astroidal Geometry of Hypocycloids and the Hessian Topology of Hyperbolic Polynomials. Moscow: Moscow Center for Continuous Mathematical Education Press, 2001 (in Russian).
2002-14
Arnold V. I. Problems to the Seminar: 15 January 2002. CEREMADE (UMR 7534), Université Paris-Dauphine, № 0216, 16/05/2002.
Arnold V. I. What Is Mathematics? Moscow: Moscow Center for Continuous Mathematical Education Press, 2002, 104 pp.
2002-14 — V. I. Arnold
Korkina E. I. Two-dimensional continued fractions. The simplest examples. Proc. Steklov Inst. Math., 1995, 209, 124–144.
2002-15
Arnold V. I. Problems to the Seminar: 15 January 2002. CEREMADE (UMR 7534), Université Paris-Dauphine, № 0216, 16/05/2002.
Arnold V. I. What Is Mathematics? Moscow: Moscow Center for Continuous Mathematical Education Press, 2002, 104 pp.
2002-15 — V. I. Arnold
Arnold V. I. Continued Fractions. Moscow: Moscow Center for Continuous Mathematical Education Press, 2001 (in Russian). (“Mathematical Education” Library, 14.)
Brodén T. Wahrscheinlichkeits Bestimmungen bei der gewöhnlichen Kettenbruchentwicklung reeller Zahlen. Akad. Föhr. Stockholm, 1900, 57, 239–266.
Kontsevich M. L., Sukhov Yu. M. Statistics of Klein polyhedra and multidimensional continued fractions. In: Pseudoperiodic Topology. Editors: V. Arnold, M. Kontsevich and A. Zorich. Providence, RI: Amer. Math. Soc., 1999, 9–27. (AMS Transl., Ser. 2, 197; Adv. Math. Sci., 46.)
Wiman A. Über eine-wahrscheinlichkeits Auflage bei Kettenbruchentwicklungen. Akad. Föhr. Stockholm, 1900, 57, 589–841.
2002-16
Arnold V. I., Krylov A. L. Uniform distribution of points on a sphere and some ergodic properties of solutions of linear ordinary differential equations in a complex region. Sov. Math. Dokl., 1963, 4(1), 1–5. [The Russian original is reprinted in: Vladimir Igorevich Arnold. Selecta-60. Moscow: PHASIS, 1997, 47–53.]
2002-22
Arnold V. I. Topology and statistics of formulae of arithmetics. Russian Math. Surveys, 2003, 58(4), 637–664.
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(2005). Comments. In: Arnold, V.I. (eds) Arnold's Problems. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-26866-9_2
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