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Book Review
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Book Information
Author(s):
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:
- 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
Additional Information:
Reviewer(s):
Philip
Holmes
Review Information:
Journal:
Bull. Amer. Math. Soc.
21
(1989),
101-105.
DOI:
10.1090/S0273-0979-1989-15775-3
PII:
S 0273-0979(1989)15775-3
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