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Chaos, Dynamics, and Fractals

An Algorithmic Approach to Deterministic Chaos

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Paperback | 25 July 1994

At a Glance

Paperback
348 Pages

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22.86 x 15.24 x 1.98

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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.

Industry Reviews

' 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

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You Can Find This Book In

Non-Fiction Mathematics Topology Science Physics Applied Mathematics Chaos Theory Calculus & Mathematical Analysis Differential Calculus & Equations Geometry Fractal Geometry

Foreword
Introduction
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
Multifractals
Statistical physics on chaotic symbol sequences
Universal chaotic dynamics
Intermittence in fluid dynamics
From flows to automata: chaotic systems as completely deterministic machines
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

Chaos, Dynamics, and Fractals

An Algorithmic Approach to Deterministic Chaos

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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