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Hamiltonian dynamical systems. A reprint selection. (English) Zbl 0628.01045

IOP Publishing Ltd. Bristol - Philadelphia: Adam Hilger. XII, 748 p. (1987).
The publication of this volume reflects the revived interest in classical mechanics in the past twenty-five years manifesting itself in an increasing number of papers on that subject. The book renders a collection of reprints of articles covering the various aspects of Hamiltonian dynamics ranging from problems of equilibria and stability of periodic orbits to chaos and stochasticity. There are two papers by Birkhoff and Hedlund dating from 1927 and 1932, respectively, some important articles from the sixties and seventies, half of the papers originating from the past seven years, the most recent ones from 1986. The first part contains five introductory articles (four of which also reprints) which give an excellent review of the main lines of research in this field. The following sections, containing original papers, deal with equilibria and periodic orbits, quasiperiodic orbits, breakup of invariant tori, chaotic behaviour, mixed systems and, finally, applications in rather different fields. The collection is valuable for anybody interested in Hamiltonian dynamical systems. Firstly, it comprises essential papers originally published in a wide range of journals including some less easily accessible ones. Secondly, the review articles provide a good introduction into the subject; this holds especially of the article by M. V. Berry; it is the most comprehensive one, and a pleasure to the reader (the pleasure being somewhat diminished by numerous misprints and permutation of columns).
Reviewer: H.Roos

MSC:

01A75 Collected or selected works; reprintings or translations of classics
01A60 History of mathematics in the 20th century
70-03 History of mechanics of particles and systems