Advertisement

Regular and Chaotic Dynamics

, Volume 13, Issue 6, pp 515–524 | Cite as

A few things I learnt from Jürgen Moser

  • A. P. VeselovEmail author
Jürgen Moser - 80

Abstract

A few remarks on integrable dynamical systems inspired by discussions with Jürgen Moser and by his work.

Key words

integrability adiabatic invariants geodesics 

MSC2000 numbers

37J35 70H11 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Moser, J. and Veselov, A. P., Discrete Versions of Some Classical Integrable Systems and Factorization of Matrix Polynomials, Comm. Math. Phys., 1991, vol. 139, pp. 217–243.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Arnold, V. I., Mathematical Methods of Classical Mechanics, Graduate Texts in Mathematics, vol. 60, New York-Heidelberg: Springer, 1978.zbMATHGoogle Scholar
  3. 3.
    Moser, J., Various Aspects of Integrable Hamiltonian Systems, Dynamical Systems (C.I.M.E. Summer School, Bressanone, 1978), pp. 233–289, Progr. Math., vol. 8, Boston, Mass.: Birkhäuser, 1980.Google Scholar
  4. 4.
    Manakov, S.V., A Remark on the Integration of the Euler Equations of the Dynamics of an Ndimensional Rigid Body, Funktsional. Anal. i Prilozhen., 1976, vol. 10, no. 4, pp. 93–94 (in Russian).zbMATHMathSciNetGoogle Scholar
  5. 5.
    Bobenko, A. I., Lorbeer B., and Suris, Yu. B., Integrable Discretizations of the Euler Top, J. Math. Phys., 1998, vol. 39, no. 12, pp. 6668–6683.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Bolsinov, A.V. and Taimanov, I.A., Integrable Geodesic Flows with Positive Topological Entropy, Invent. Math., 2000, vol. 140, no. 3, pp. 639–650.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Birkhoff, G.D., Dynamical Systems, With an addendum by Jürgen Moser, AMS Colloquium Publications, vol. 9, Providence, R. I.: AMS, 1966.zbMATHGoogle Scholar
  8. 8.
    Kozlov, V.V., Topological Obstacles to the Integrability of Natural Mechanical Systems, Dokl. Akad. Nauk SSSR, 1979, vol. 249, no. 6, pp. 1299–1302 (in Russian).MathSciNetGoogle Scholar
  9. 9.
    Milnor, J., On Lattès Maps, in Dynamics on the Riemann sphere, Zürich: Eur. Math. Soc., 2006, pp. 9–43.Google Scholar
  10. 10.
    Veselov, A. P., Integrable Mappings, Uspekhi Mat. Nauk, 1991, vol.46, no. 5(281), pp. 3–45, 190 [Russian Math. Surveys, 1991, vol. 46, no. 5, pp. 1–51].zbMATHMathSciNetGoogle Scholar
  11. 11.
    Moser, J., Regularization of Kepler’s Problem and the Averaging Method on a Manifold, Comm. Pure Appl. Math., 1970, vol. 23, pp. 609–636.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Knörrer, H., Geodesics on Quadrics and a Mechanical Problem of C. Neumann, J. Reine Angew. Math., 1982, vol. 334, pp. 69–78.zbMATHMathSciNetGoogle Scholar
  13. 13.
    Moser, J., Integrable Hamiltonian Systems and Spectral Theory, Pisa: Lezioni Fermiane, 1981.zbMATHGoogle Scholar
  14. 14.
    Topalov, P. and Matveev, V. S., Geodesic Equivalence via Integrability, Geom. Dedicata, 2003, vol. 96, pp. 91–115.zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Tabachnikov, S., Projectively Equivalent Metrics, Exact Transverse Line Fields and the Geodesic Flow on the Ellipsoid, Comment. Math. Helv., 1999, vol. 74, no. 2, pp. 306–321.zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Khesin, B. and Tabachnikov, S., Spaces of Pseudo-Riemannian Geodesics and Pseudo-Euclidean Billiards, http://arxiv.org/abs/math.DG/0608620.
  17. 17.
    Cao, C., Stationary Harry-Dym’s Equation and its Relation with Geodesics on Ellipsoid, Acta Math. Sinica, 1990, vol. 6, no. 1, pp. 35–41.zbMATHMathSciNetGoogle Scholar
  18. 18.
    Veselov, A.P., Two Remarks about the Connection of Jacobi and Neumann Integrable Systems, Math. Z., 1994, vol. 216, pp. 337–345.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  1. 1.Department of Mathematical SciencesLoughborough UniversityLoughboroughUK
  2. 2.Landau Institute for Theoretical PhysicsMoscowRussia

Personalised recommendations