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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Full text of review: PDF

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, vol. 59, Springer-Verlag, New York, 1985. MR 810620 (87d:34065)
  • 4. V. I. Arnold, Mathematical methods of classical mechanics, Springer-Verlag, New York-Heidelberg, 1978. Translated from the Russian by K. Vogtmann and A. Weinstein; Graduate Texts in Mathematics, 60. MR 0690288 (57 #14033b)
  • 5. N. N. Nehorošev, An exponential estimate of the time of stability of nearly integrable Hamiltonian systems. II, Trudy Sem. Petrovsk. 5 (1979), 5–50 (Russian). MR 549621 (80m:58017)
  • 6. John Guckenheimer and Philip Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Applied Mathematical Sciences, vol. 42, Springer-Verlag, New York, 1983. MR 709768 (85f:58002)
  • 7. E. A. Grebenikov and Yu. A. Ryabov, Constructive methods in the analysis of nonlinear systems, “Mir”, Moscow;\ distributed by Imported Publications, Chicago, IL, 1983. Translated from the Russian by Ram S. Wadhwa. MR 733787 (85j:34003)
  • 8. V. I. Arnol′d, Geometrical methods in the theory of ordinary differential equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 250, Springer-Verlag, New York-Berlin, 1983. Translated from the Russian by Joseph Szücs; Translation edited by Mark Levi. MR 695786 (84d:58023)
  • 9. Richard H. Rand and Dieter Armbruster, Perturbation methods, bifurcation theory and computer algebra, Applied Mathematical Sciences, vol. 65, Springer-Verlag, New York, 1987. MR 911274 (89a:58083)
  • 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), no. 1, 15–27. MR 777620 (86g:81034)


Review Information

Reviewer: Philip Holmes
Journal: Bull. Amer. Math. Soc. 21 (1989), 101-105
DOI: http://dx.doi.org/10.1090/S0273-0979-1989-15775-3
PII: S 0273-0979(1989)15775-3