Customer Reviews

Deterministic chaos: An introduction

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In the eighties, when many of us were trying to learn nonlinear dynamics (by teaching it) from outdated texts on nonlinear differential equations (no chaos theory) and newer research papers, this book was extremely helpful. In contrast with Lichtenberg and Lieberman, which preceded it (and was for a few years the only modern book on chaos available), it did not ignore driven-dissipative systems but rather emphasized them. Still provides a good introduction for a beginner (when one supplements it by going to the orginal literature), although I would of course recommend my own books on the subject, especially with regard to understanding what is meant by integrability/nonintegrability, what is meant by a 'chaotic orbit', and to avoid confusing randomness with deterministic chaos. It is a disease with all books on chaos that the writers do not advise the student to do backard in time integration to check the validity of forward time numerical integrations. therefore, the cookbook recipe given in those texts for calculating Liapunov exponents is wrong and misleading. Another way to say it is that deterministic chaos is not developed from the systematic standpoint of symbollic dynamics in those texts, but rather from the standpoint of meaningless numerical integrations packed full with machine errors.