Deterministic Chaos: An Introduction [Hardcover]

Heinz Georg Schuster (Author)

Book Description

Publication Date: November 1987

This revised and updated version of a classic introduction to deterministic chaos views the field from a physicist's point of view. This edition contains new sections on sensitive parameter dependence, fat fractals, characterization of attractors by scaling indices, the Farey tree, and the notion of global universality. The book answers basic questions such as what is deterministic chaos, how is it generated, where does it occur, and what can one learn from a chaotic signal? It also explains advanced concepts such as bifurcations, intermittency, Liapunov exponents, functional renormalization groups, and strange attractors. The book requires no background beyond that possessed by a graduate student in physics.

Editorial Reviews

Review

The book gives a self-contained introduction to the modern nonlinear dynamics physicist's point of view. The basic concepts and methods of this theory, such as Lyapunov exponents, dimensions, Kolmogorov's entropy, strange attractors, KAM-theory, Arnold diffusion, renormalization group theory, etc. are introduced and explained on an elementary level. Moreover, the general models of transition from order to chaos (period doubling, intermittency, Ruele-Takens model), chaos in quantum systems and the problems of controlling chaos are also discussed. The above material is explained and illustrated by a great number of concrete examples of chaotic dynamical systems arising in applications for which a detailed theoretical and numerical study is given.
For reviews of earlier editions see Zbl 707.580004 (1st ed. 1984), Zbl 707.58003 (2nd ed. 1988), Zbl 709.58002 (1st reprint of 2nd ed. 1989
Serguei Zelik (Moskva)
published Zentralblatt f?r Mathematik, Springer, iss. April 2001 --This text refers to an out of print or unavailable edition of this title.

From the Back Cover

Heinz Georg Schuster Deterministic Chaos An Introduction This third edition of Deterministic Chaos has been updated and augmented with an extra chapter on "controlling chaos". Deterministic Chaos has been translated into Japanese, Chinese, Russian, Polish, and German, and has become a standard text for students and researchers who need a concise introduction into the field of chaos. From reviews of a previous edition: In this book, Schuster gives a very useful summary of the main ideas of the subject as it now stands. Although a physicist by training and style, he organizes his treatment by the logic of the mathematics, which is based on the concept of a dynamical system. Students about to begin research into chaos, and practising scientists new to the subject, will find this book well worth reading. Nature This text sets a standard which other authors and publishers in physics should strive to meet. Physics Bulletin --This text refers to an out of print or unavailable edition of this title.

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Product Details

• Hardcover: 296 pages
• Publisher: Wiley-VCH Verlag GmbH; 2nd edition (November 1987)
• Language: English
• ISBN-10: 3527268626
• ISBN-13: 978-3527268627
• Product Dimensions: 9.4 x 6.8 x 0.9 inches
• Shipping Weight: 1.8 pounds
• Average Customer Review: 3.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #3,863,333 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

3 of 5 people found the following review helpful:

3.0 out of 5 stars Was a real help in the mid-eighties, May 12, 2002

By 

Professor Joseph L. McCauley "Joseph L. McCauley" (Austria+Texas) - See all my reviews

This review is from: Deterministic Chaos: An Introduction (Hardcover)

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.