Chaos and integrability in nonlinear dynamics. An introduction. (English) Zbl 0682.58003

Wiley-Interscience Publications. New York etc.: John Wiley & Sons. xiii, 364 p. £35.15 (1989).
The purpose of the book under review is to close the gap between the modern mathematical theory of dynamical systems and its applications in physics. The author does not intend to prove theorems, but to discuss important notions and results as well as their historical developments (mostly seen from the physicist’s point of view). The book is well- written, numerical examples are given and a lot of “pictures” do illustrate the results.
The main chapter headings are as follows: 1. The dynamics of differential equations. 2. Hamiltonian dynamics. 3. Classical perturbation theory (including the KAM-theorem). 4. Chaos in Hamiltonian systems and area- preserving mappings. 5. The dynamics of dissipative systems. 6. Chaos and integrability in Semiclassical mechanics. 7. Nonlinear evolution equations and solitons. 8. Analytic structure of dynamical systems.
Reviewer: N.Jacob


58-02 Research exposition (monographs, survey articles) pertaining to global analysis
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37C75 Stability theory for smooth dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C99 Qualitative theory for ordinary differential equations