Chaos Theory Tamed

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Overview

Williams uses lists, graphics, examples, and friendly language to help readers understand the vocabulary and significance of chaos theory. The book will help scientists and students outside mathematics to use the concepts of chaos in working with data and will help interested lay readers grasp the fundamentals.
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Editorial Reviews

Booknews
A semitechnical introduction to what has become the new paradigm in the realm of mathematics. The author comes from a peripheral field geology/hydrology and writes with an informal style; no prior knowledge of chaos theory is assumed. Intended for those without a strong mathematics and physics background, this survey nevertheless does require persistence and motivation on the reader's part along with some familiarity through introductory courses with algebra, trigonometry geometry, and statistics. After introductory background chapters, he offers a foundation of selected important material from various fields, followed by more advanced concepts. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780309063517
  • Publisher: National Academies Press
  • Publication date: 10/8/1997
  • Series: Chaos Theory Series
  • Pages: 29
  • Product dimensions: 6.34 (w) x 9.40 (h) x 1.28 (d)

Table of Contents

Preface
Symbols
1 Introduction 3
2 Chaos in perspective 9
3 Phase space - the playing field 23
4 Distances and lines in space 35
5 Vectors 49
6 Probability and information 65
7 Autocorrelation 97
8 Fourier analysis 107
9 Preliminary analysis of time-series data 131
10 The parameter as king 161
11 Nonchaotic attractors 175
12 Routes to chaos 189
13 Chaotic equations 203
14 Sensitive dependence on initial conditions 211
15 The chaotic (strange) attractor 221
16 Order within chaos 229
17 Fractal structure 237
18 Uncovering determinism 247
19 Attractor reconstruction 265
20 Background information on dimensions 291
21 Similarity dimension 301
22 Capacity and Hausdorff dimension 315
23 Information dimension 321
24 Correlation dimension 329
25 Lyapunov exponents 353
26 Kolmogorov - Sinai entropy 381
27 Mutual information and redundancy 407
Epilogue 443
Appendix Selected laws of powers, roots and logarithms 445
Glossary 447
References 471
Index 485
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