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Chaos, Dynamics, and Fractals : An Algorithmic Approach to Deterministic Chaos - Joseph L. McCauley

Chaos, Dynamics, and Fractals

An Algorithmic Approach to Deterministic Chaos


Published: 25th July 1994
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This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the method of analysis and choice of emphasis make it very different from all other books in the field. It is written to provide the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects such as universal critical exponents, devil's staircases, and the Farey tree. Throughout the book the author uses a fully discrete method, a "theoretical computer arithmetic," because finite (but not fixed) precision is a fact of life that cannot be avoided in computation or in experiment. This approach leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The author explains why continuum analysis, computer simulations, and experiments form three entirely distinct approaches to chaos theory. In the end, the connection is made with Turing's ideas of computable numbers. It is explained why the continuum approach leads to predictions that are not necessarily realized in computations or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed.

' a very readable account ... an excellent introduction to fractals and deterministic chaos ...' Chemistry in Britain 'very well written' Journal of the Association of C and C++ Users

Flows in phase space
Introduction to deterministic chaos
Conservative synamical systems
Fractals and fragmentation in phase space
The way to chaos by instability of quasiperiodic orbits
The way to chaos by period doubling
Statistical physics on chaotic symbol sequences
Universal chaotic dynamics
Intermittence in fluid dynamics
From flows to automata: chaotic systems as completely deterministic machines
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521467476
ISBN-10: 0521467470
Series: Cambridge Nonlinear Science
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 348
Published: 25th July 1994
Country of Publication: GB
Dimensions (cm): 22.66 x 15.27  x 2.06
Weight (kg): 0.49