Items related to Deterministic Chaos: An Introduction
Synopsis
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.
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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 für Mathematik, Springer, iss. April 2001
A self–contained introduction to the modern nonlinear dynamics
Serguei Zelik (Moskva), published Zentralblatt für Mathematik, Springer, April 2001
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
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