動(dòng)力系統(tǒng)中的混沌

內(nèi)容概要

這是一本非線性動(dòng)力學(xué)方面的研究生教材，也是科研人員使用的一本很好的參考書。本書原版于1993年出版后很受歡迎，多次重印。第2版對(duì)第1版的內(nèi)容和習(xí)題都作了增補(bǔ)，并增加了第10章（混沌的控制和同步），其它章也增加了許多新內(nèi)容，如吸引域、球耦合振子的鎖相、拉格朗日流的流體平流的分形問題、奇異非混沌吸引子等。

書籍目錄

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 chaoticsystems5 Nonattraeting chaotic sets6 Quasiperiodicity7 Chaos in Hamiltonlan systems8 Chaotic transitions9 Multifractals10 Control and synchronization of chaos11 QuantumchaosReferencesIndex

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