Bulletin of the American Mathematical Society

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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.

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.

J. A. Sanders and F. Verhulst, Averaging methods in nonlinear dynamical systems, Applied Mathematical Sciences, vol. 59, Springer-Verlag, New York, 1985. MR 810620, DOI 10.1007/978-1-4757-4575-7

V. Arnold, Les méthodes mathématiques de la mécanique classique, Éditions Mir, Moscow, 1976 (French). Traduit du russe par Djilali Embarek. MR 0474391

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

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, DOI 10.1007/978-1-4612-1140-2

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

V. I. Arnol′d, Geometrical methods in the theory of ordinary differential equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 250, Springer-Verlag, New York-Berlin, 1983. Translated from the Russian by Joseph Szücs; Translation edited by Mark Levi. MR 695786

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, DOI 10.1007/978-1-4612-1060-3

10.

J. E. Marsden and T. S. Ratiu, Mechanics and symmetry, forthcoming book.

M. V. Berry, Classical adiabatic angles and quantal adiabatic phase, J. Phys. A 18 (1985), no. 1, 15–27. MR 777620

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 0810620

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