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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.
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1958-2 — S. A. Bogatyĭ
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1958-2 — S. M. Gusein-Zade
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1958-3 — S. Yu. Yakovenko
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1963-1
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1963-1 — V. I. Arnold
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1963-1 — M. B. Sevryuk
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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.
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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.
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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).
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Koch H. A renormalization group for Hamiltonians, with applications to KAM tori. Ergod. Theory Dynam. Systems, 1999, 19(2), 475–521.
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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.
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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.
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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.
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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.)
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Fassò F., Guzzo M., Benettin G. Nekhoroshev-stability of elliptic equilibria of Hamiltonian systems. Commun. Math. Phys., 1998, 197(2), 347–360.
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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.
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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.
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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.)
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Lochak P., NeĬshtadt A. I., Estimates of stability time for nearly integrable systems with a quasiconvex Hamiltonian. Chaos, 1992, 2(4), 495–499.
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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.
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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.
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