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A few things I learnt from Jürgen Moser. (English) Zbl 1229.37076

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

MSC:

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
70H11 Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics
01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

Moser, Jürgen
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References:

[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. · Zbl 0754.58017 · doi:10.1007/BF02352494
[2] Arnold, V. I., Mathematical Methods of Classical Mechanics, Graduate Texts in Mathematics, vol. 60, New York-Heidelberg: Springer, 1978. · Zbl 0386.70001
[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.
[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). · Zbl 0343.70003
[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. · Zbl 0944.70009 · doi:10.1063/1.532648
[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. · Zbl 0985.37027 · doi:10.1007/s002220000066
[7] Birkhoff, G.D., Dynamical Systems, With an addendum by Jürgen Moser, AMS Colloquium Publications, vol. 9, Providence, R. I.: AMS, 1966.
[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).
[9] Milnor, J., On Lattès Maps, in Dynamics on the Riemann sphere, Zürich: Eur. Math. Soc., 2006, pp. 9–43. · Zbl 1235.37015
[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].
[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. · Zbl 0193.53803 · doi:10.1002/cpa.3160230406
[12] Knörrer, H., Geodesics on Quadrics and a Mechanical Problem of C. Neumann, J. Reine Angew. Math., 1982, vol. 334, pp. 69–78.
[13] Moser, J., Integrable Hamiltonian Systems and Spectral Theory, Pisa: Lezioni Fermiane, 1981. · Zbl 0527.70022
[14] Topalov, P. and Matveev, V. S., Geodesic Equivalence via Integrability, Geom. Dedicata, 2003, vol. 96, pp. 91–115. · Zbl 1017.37029 · doi:10.1023/A:1022166218282
[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. · Zbl 0958.37008 · doi:10.1007/s000140050091
[16] Khesin, B. and Tabachnikov, S., Spaces of Pseudo-Riemannian Geodesics and Pseudo-Euclidean Billiards, http://arxiv.org/abs/math.DG/0608620 . · Zbl 1173.37037
[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. · Zbl 0705.35123
[18] Veselov, A.P., Two Remarks about the Connection of Jacobi and Neumann Integrable Systems, Math. Z., 1994, vol. 216, pp. 337–345. · Zbl 0815.58011 · doi:10.1007/BF02572325
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