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力学基础与工程技术前沿
Hyperbolic Chaos: A Physicist`s View双曲混
作 者:
Sergey P. Kuznetsov
ISBN:978-7-04-031964-4 出版时间:2011-09-14
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Front Matter
Part I Basic Notions and Review
1 Dynamical Systems and Hyperbolicity
2 Possible Occurrence of Hyperbolic Attractors
Part II Low-Dimensional Models
3 Kicked Mechanical Models and Differential Equations with Periodic Switch
4 Non-Autonomous Systems of Coupled Self-Oscillators
5 Autonomous Low-dimensional Systems with Uniformly Hyperbolic Attractors in the Poincar´e Maps
6 Parametric Generators of Hyperbolic Chaos
7 Recognizing the Hyperbolicity: Cone Criterion and Other Approaches
Part III Higher-Dimensional Systems and Phenomena
8 Systems of Four Alternately Excited Non-autonomous Oscillators
9 Autonomous Systems Based on Dynamics Close to Heteroclinic Cycle
10 Systems with Time-delay Feedback
11 Chaos in Co-operative Dynamics of Alternately Synchronized Ensembles of Globally Coupled Self-oscillators
Part IV Experimental Studies
12 Electronic Device with Attractor of Smale-Williams Type
13 Delay-time Electronic Devices Generating Trains of Oscillations with Phases Governed by Chaotic Maps
14 Conclusion
Appendix A Computation of Lyapunov Exponents:The Benettin Algorithm
Appendix B H´enon and Ikeda Maps
Appendix C Smale’s Horseshoe and Homoclinic Tangle
Appendix D Fractal Dimensions and Kaplan-Yorke Formula
Appendix E Hunt’s Model: Formal Definition
Appendix F Geodesics on a Compact Surface of Negative Curvature
AppendixG Effect of Noise in a System with a Hyperbolic Attractor
Index
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