| Preface to the first edition Preface to the second edition 1 Introduction and overview 1.1 Some history. 1.2 Examples of chaotic behavior 1.3 Dynamical systems 1.4 Attractors 1.5 Sensitive dependence on initial conditions 1.6 Delay coordinates Problems Notes 2 One-dimensional maps 2.1 Piecewise linear one-dimensional maps 2.2 The logistic map 2.3 General discussion of smooth one-dimensional maps 2.4 Examples of applications of one-dimensional maps to chaotic systems of higher dimensionaiity Appendix: Some elementary definitions and theorems concerning sets Problems Notes 3 Strange attractors and fractal dimension 3.1 The box-counting dimension 3.2 The generalized baker's map 3.3 Measure and the spectrum of Dq dimensions 3.4 Dimension spectrum for the generalized baker's map 3.5 Character of the natural measure for the generalized baker's map 3.6 The pointwise dimension …… 4 Dynamical properties of chaoticsystems 5 Nonattraeting chaotic sets 6 Quasiperiodicity 7 Chaos in Hamiltonlan systems 8 Chaotic transitions 9 Multifractals 10 Control and synchronization of chaos 11 Quantumchaos References Index |
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