Abstract
A few remarks on integrable dynamical systems inspired by discussions with Jürgen Moser and by his work.
Similar content being viewed by others
References
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.
Arnold, V. I., Mathematical Methods of Classical Mechanics, Graduate Texts in Mathematics, vol. 60, New York-Heidelberg: Springer, 1978.
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.
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).
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.
Bolsinov, A.V. and Taimanov, I.A., Integrable Geodesic Flows with Positive Topological Entropy, Invent. Math., 2000, vol. 140, no. 3, pp. 639–650.
Birkhoff, G.D., Dynamical Systems, With an addendum by Jürgen Moser, AMS Colloquium Publications, vol. 9, Providence, R. I.: AMS, 1966.
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).
Milnor, J., On Lattès Maps, in Dynamics on the Riemann sphere, Zürich: Eur. Math. Soc., 2006, pp. 9–43.
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].
Moser, J., Regularization of Kepler’s Problem and the Averaging Method on a Manifold, Comm. Pure Appl. Math., 1970, vol. 23, pp. 609–636.
Knörrer, H., Geodesics on Quadrics and a Mechanical Problem of C. Neumann, J. Reine Angew. Math., 1982, vol. 334, pp. 69–78.
Moser, J., Integrable Hamiltonian Systems and Spectral Theory, Pisa: Lezioni Fermiane, 1981.
Topalov, P. and Matveev, V. S., Geodesic Equivalence via Integrability, Geom. Dedicata, 2003, vol. 96, pp. 91–115.
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.
Khesin, B. and Tabachnikov, S., Spaces of Pseudo-Riemannian Geodesics and Pseudo-Euclidean Billiards, http://arxiv.org/abs/math.DG/0608620.
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.
Veselov, A.P., Two Remarks about the Connection of Jacobi and Neumann Integrable Systems, Math. Z., 1994, vol. 216, pp. 337–345.
Author information
Authors and Affiliations
Corresponding author
Additional information
To the dear memory of Jürgen Moser
Rights and permissions
About this article
Cite this article
Veselov, A.P. A few things I learnt from Jürgen Moser. Regul. Chaot. Dyn. 13, 515–524 (2008). https://doi.org/10.1134/S1560354708060038
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1560354708060038