Overview

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.

Full Product Details

Author:   Sergey P. Kuznetsov
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2012
ISBN:  

9783642236655

ISBN 10:   3642236650
Pages:   336
Publication Date:   15 November 2011
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

Part I Basic Notions and Review: Dynamical Systems and Hyperbolicity.- Dynamical Systems and Hyperbolicity.- Part II Low-Dimensional Models: Kicked Mechanical Models and Differential Equations with Periodic Switch.- Non-Autonomous Systems of Coupled Self-Oscillators.- Autonomous Low-dimensional Systems with Uniformly Hyperbolic Attractors in the Poincar'e Maps.- Parametric Generators of Hyperbolic Chaos.- Recognizing the Hyperbolicity: Cone Criterion and Other Approaches.- Part III Higher-Dimensional Systems and Phenomena: Systems of Four Alternately Excited Non-autonomous Oscillators.- Autonomous Systems Based on Dynamics Close to Heteroclinic Cycle.- Systems with Time-delay Feedback.- Chaos in Co-operative Dynamics of Alternately Synchronized Ensembles of Globally Coupled Self-oscillators.- Part IV Experimental Studies: Electronic Device with Attractor of Smale-Williams Type.- Delay-time Electronic Devices Generating Trains of Oscillations with Phases Governed by Chaotic Maps.

Reviews

From the reviews: The material presented in this book shows significant progress in the main directions of the research program aimed at establishing better links between the abstract theory of hyperbolic systems and real examples of chaotic systems. Each chapter supplies a wealth of references for further studies . This monograph will be useful for mathematicians interested in applications of the theory of hyperbolic attractors, as well as for physicists and engineers dealing with real life applications of the theory of deterministic chaos. (Yuri V. Rogovchenko, Zentralblatt MATH, Vol. 1239, 2012) From the reviews: The material presented in this book shows significant progress in the main directions of the research program aimed at establishing better links between the abstract theory of hyperbolic systems and real examples of chaotic systems. Each chapter supplies a wealth of references for further studies . This monograph will be useful for mathematicians interested in applications of the theory of hyperbolic attractors, as well as for physicists and engineers dealing with real life applications of the theory of deterministic chaos. (Yuri V. Rogovchenko, Zentralblatt MATH, Vol. 1239, 2012)

From the reviews: </p> The material presented in this book shows significant progress in the main directions of the research program aimed at establishing better links between the abstract theory of hyperbolic systems and real examples of chaotic systems. Each chapter supplies a wealth of references for further studies . This monograph will be useful for mathematicians interested in applications of the theory of hyperbolic attractors, as well as for physicists and engineers dealing with real life applications of the theory of deterministic chaos. (Yuri V. Rogovchenko, Zentralblatt MATH, Vol. 1239, 2012)</p>

From the reviews: The material presented in this book shows significant progress in the main directions of the research program aimed at establishing better links between the abstract theory of hyperbolic systems and real examples of chaotic systems. Each chapter supplies a wealth of references for further studies . This monograph will be useful for mathematicians interested in applications of the theory of hyperbolic attractors, as well as for physicists and engineers dealing with real life applications of the theory of deterministic chaos. (Yuri V. Rogovchenko, Zentralblatt MATH, Vol. 1239, 2012)

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