Hyperbolic Chaos: A Physicist’s View

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Springer Science & Business Media, Mar 20, 2012 - Science - 320 pages
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"Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos.

This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering.

Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia.

 

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Contents

Part II LowDimensional Models
57
Part III HigherDimensional Systems and Phenomena
171
Part IV Experimental Studies
257
The Benettin Algorithm
277
Appendix B Hénon and Ikeda Maps
281
Appendix C Smales Horseshoe and Homoclinic Tangle
289
Appendix D Fractal Dimensions and KaplanYorke Formula
293
Formal Definition
298
Appendix F Geodesics on a Compact Surface of Negative Curvature
305
Appendix G Effect of Noise in a System with a Hyperbolic Attractor
310
Index
318
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