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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Book Information:

Author: V. I. Arnold
Title: Mathematical methods of classical mechanics
Additional book information: translated from the 1974 Russian edition by K. Vogtmann and A. Weinstein, Graduate Texts in Math., Vol. 60, Springer-Verlag, New York and Berlin, 1978, x + 462 pp.

Author: Walter Thirring
Title: A course in mathematical physics, vol. 1: Classical dynamical systems
Additional book information: translated from German by Evans M. Harrel, Springer-Verlag, New York and Berlin, 1978, xii + 258 pp., $19.80.

References [Enhancements On Off] (What's this?)

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  • 2. V. I. Arnol′d, Proof of a theorem of A. N. Kolmogorov on the preservation of conditionally periodic motions under a small perturbation of the Hamiltonian, Uspehi Mat. Nauk 18 (1963), no. 5 (113), 13–40 (Russian). MR 0163025
  • 3. V. I. Arnol′d and A. Avez, Ergodic problems of classical mechanics, Translated from the French by A. Avez, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0232910
  • 4. Stefan Banach, Mechanics, Monografie Matematyczne. Tom XXIV, Polskie Towarzystwo Matematyczne, Warszawa-Wroclaw, 1951. Translated by E. J. Scott. MR 0043607
  • 5. G. D. Birkhoff, Dynamical systems, Amer. Math. Soc. Colloq. Publ., vol. 9, Amer. Math. Soc., New York, 1927.
  • 6. A. N. Kolmogorov, General theory of dynamical systems, Proc. Internat. Congr. Math. (Amsterdam, 1954), vol. 1, North-Holland, Amsterdam, 1957, p. 315. (Russian)
  • 7. A. N. Kolmogorov, On conservation of conditionally periodic motions for a small change in Hamilton’s function, Dokl. Akad. Nauk SSSR (N.S.) 98 (1954), 527–530 (Russian). MR 0068687
  • 8. Cornelius Lanczos, The Variational Principles of Mechanics, Mathematical Expositions, no. 4, University of Toronto Press, Toronto, Ont., 1949. MR 0034139
  • 9. Lynn H. Loomis and Shlomo Sternberg, Advanced calculus, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1968. MR 0227327
  • 10. S. Mac Lane, Geometrical mechanics, mimeographed notes, Dept. of Mathematics, Chicago University, 1968.
  • 11. J. Moser, On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1962 (1962), 1–20. MR 0147741
  • 12. Jürgen Moser, Stable and random motions in dynamical systems, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1973. With special emphasis on celestial mechanics; Hermann Weyl Lectures, the Institute for Advanced Study, Princeton, N. J; Annals of Mathematics Studies, No. 77. MR 0442980
  • 13. E. Noether, Invariante Variationsproblem, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. 2 (1918), 235.
  • 14. L. A. Pars, A treatise on analytical dynamics, Heinemann, London, 1965.
  • 15. H. Poincaré, Les méthodes nouvelles de la mécanique celeste, 3 vols., reprint, Dover, New York, 1957.
  • 16. Carl Ludwig Siegel and Jürgen K. Moser, Lectures on celestial mechanics, Springer-Verlag, New York-Heidelberg, 1971. Translation by Charles I. Kalme; Die Grundlehren der mathematischen Wissenschaften, Band 187. MR 0502448
  • 17. S. Sternberg, Celestial mechanics, 2 vols., Benjamin, New York, 1969.
  • 18. J. L. Synge, Classical Dynamics, Handbuch der Physik, Bd. III/1, Springer, Berlin, 1960, pp. 1–225. MR 0117945
  • 19. E. T. Whittaker, A treatise on the analytical dynamics of particles and rigid bodies: With an introduction to the problem of three bodies, 4th ed, Cambridge University Press, New York, 1959. MR 0103613
  • 20. A. Winter, The analytical foundatons of celestial mechanics, Princeton Univ. Press, Princeton, N. J., 1947.

Review Information:

Reviewer: Ian N. Sneddon
Journal: Bull. Amer. Math. Soc. 2 (1980), 346-352