ABSTRACT

This text aims to bridge the gap between non-mathematical popular treatments and the distinctly mathematical publications that non- mathematicians find so difficult to penetrate. The author provides understandable derivations or explanations of many key concepts, such as Kolmogrov-Sinai entropy, dimensions, Fourier analysis, and Lyapunov exponents.

part |2 pages

PART I: BACKGROUND

chapter 1|6 pages

Introduction

chapter 2|12 pages

Chaos in perspective

part |2 pages

PART II: THE AUXILIARY TOOLKIT

chapter 3|12 pages

Phase space—the playing field

chapter 4|14 pages

Distances and lines in space

chapter 5|16 pages

Vectors

chapter 6|32 pages

Probability and information

chapter 7|10 pages

Autocorrelation

chapter 8|24 pages

Fourier analysis

chapter 9|28 pages

Preliminary analysis of time-series data

part |2 pages

PART III: HOW TO GET THERE FROM HERE

chapter 10|14 pages

The parameter as king

chapter 11|14 pages

Nonchaotic attractors

chapter 12|14 pages

Routes to chaos

chapter 13|6 pages

Chaotic equations

part |2 pages

PART IV: CHARACTERISTICS OF CHAOS

chapter 14|10 pages

Sensitive dependence on initial conditions

chapter 15|8 pages

The chaotic (strange) attractor

chapter 16|8 pages

Order within chaos

chapter 17|8 pages

Fractal structure

part |2 pages

PART V: PHASE SPACE SIGNATURES

chapter 18|18 pages

Uncovering determinism

chapter 19|26 pages

Attractor reconstruction

chapter 20|10 pages

Background information on dimensions

chapter 21|14 pages

Similarity dimension

chapter 22|6 pages

Capacity and Hausdorff dimension

chapter 23|8 pages

Information dimension

chapter 24|22 pages

Correlation dimension

part |2 pages

PART VII: QUANTITATIVE MEASURES OF CHAOS

chapter 25|28 pages

Lyapunov exponents

chapter 26|26 pages

Kolmogorov-Sinai entropy

chapter 27|36 pages

Mutual information and redundancy