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Book Review

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Book Information:

Authors: Pierre Lochak and Claude Meunier
Title: Multiphase averaging for classical systems, with applications to adiabatic theorems
Additional book information: (Translated by H. S. Dumas), Applied Mathematical Sciences, vol. 72, Springer-Verlag, New York, Berlin, Heidelberg, 1988, xi + 360 pp., $39.80. ISBN 0-387-96778-8.

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

  • 1. N. M. Krylov and N. N. Bogoliubov, Introduction to nonlinear mechanics, Moscow, 1937. English translation, Princeton Univ. Press, Princeton, New Jersey, 1947.
  • 2. N. N. Bogoliubov and Y. A. Mitropolski, Asymptotic methods in the theory of nonlinear oscillations, Moscow, 1958. English translation, Gordon and Breach, New York, 1964.
  • 3. J. A. Sanders and F. Verhulst, Averaging methods in nonlinear dynamical systems, Applied Mathematical Sciences, no. 59, Springer-Verlag, New York, 1985. MR 810620
  • 4. V. I. Arnold, Mathematical methods of classical mechanics, Graduate Texts in Math., vol. 60, Springer-Verlag, New York, 1978. MR 690288
  • 5. N. N. Nekhoroshev, An exponential estimate of the time of stability of nearly integrable Hamiltonian systems, Russian Math. Surveys 32 (6) (1979), 1-65. MR 549621
  • 6. J. Guckenheimer and P. Holmes, Nonlinear oscillations, dynamical systems and bifurcations of vector fields, Applied Mathematical Sciences no. 42, Springer-Verlag, New York, 1983. MR 709768
  • 7. E. A. Grebenikov and Y. A. Rabov, Constructive methods in the analysis of nonlinear systems, English translation, Mir Publishers, Moscow, 1983. MR 733787
  • 8. V. I. Arnold, Geometrical methods in the theory of ordinary differential equations, Grundlehren Math. Wiss. vol. 250, Springer-Verlag, New York, 1983. MR 695786
  • 9. R. H. Rand and D. Armbruster, Perturbation methods, bifurcation theory and computer algebra, Applied Mathematical Sciences no. 65, Springer-Verlag, New York, 1987. MR 911274
  • 10. J. E. Marsden and T. S. Ratiu, Mechanics and symmetry, forthcoming book.
  • 11. M. V. Berry, Classical adiabatic angles and quantal adiabatic phase, J. Phys. A. 18 (1985), 15-27. MR 777620

Review Information:

Reviewer: Philip Holmes
Journal: Bull. Amer. Math. Soc. 21 (1989), 101-105
DOI: https://doi.org/10.1090/S0273-0979-1989-15775-3
American Mathematical Society