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Book review

Author(s) Lichtenberg, A.J.
Lieberman, M.A.
Title Regular and chaotic dynamics, 2nd ed.
Publisher Springer
Year of publication 1992
Reviewed by Heinz Ulbricht

The present volume is the 2nd revised and expanded edition of "Regular and stochastic motion" which was published in the Applied Mathematical Sciences series, vol. 38, 1983. The new title considers the development of the last 10 years and emphasizes more dissipative dynamics, circle maps, intermittancy, crises, transient chaos, multifractals, reconstruction, and coupled mapping systems.

After an introductory part the following two chapters are dedicated the canonical perturbation theory and the context of mappings and linear stability. Transition to global stochasticity, stochastic motion and problems of three and more degrees of freedom are the main topics in chapters 4, 5, 6. The last parts contain an extensive introduction to bifurcation phenomena, transition to chaos in dissipative systems and to chaotic motion. In a short appendix some aspects of planetary motion, accelerators and beams, charged particle confinement, chemical dynamics and of quantum systems are mentioned without any attempt at completeness.

The authors emphasise physical insight rather than mathematical rigor and rely heavily on numerical computations to illustrate the methods and to validate them.

The book has a high level and demonstrates that the authors are specialists in their fields.

Production and print have an excellent quality. There are a very extensive bibliography and good author and subject indices.

The book is a self-contained text and exhaustive for the topics it deals with. It is surely very useful for physical scientists and engineers familiar with the methods, but also for students and graduates who wish to enter the field. Relevant libaries are well advised to purchase this volume.