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World Scientific, 2011 · 472 pages
World Scientific Series on Nonlinear Science, Series A
ISBN 978-981-4374-07-1 (hardcover)
ISBN 978-981-4458-09-2 (ebook)
The first textbook devoted entirely to robust chaos — chaos with no periodic windows and no coexisting attractors
Its definition, sources and roles, from pure mathematics to natural and social processes
Hyperbolic systems, Lorenz-type systems, one-dimensional maps and piecewise-smooth maps
More than 260 exercises and open problems
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Robust Chaos and its Applications
Elhadj Zeraoulia and J. C. Sprott
Emeritus Professor of Physics, University of Wisconsin–Madison
Praise for Robust Chaos and its Applications
"The book is the first textbook entirely devoted to the understanding and prediction of robust chaos, with motivations and applications in real-world dynamical systems. The material of the book is presented in a rather self-contained and pedagogical style and includes exercises for students as well as advanced questions and open problems for researchers."
— Mathematical Reviews Clippings
About the Book
Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. It is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject.
Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mathematical to natural and social processes displaying robust chaos, are discussed in detail. At the end of each chapter is a set of exercises and open problems (more than 260 in the whole book) intended to reinforce the ideas and provide additional experience for readers and researchers in nonlinear science and chaos theory.
Contents
1. Poincaré Map Technique, Smale Horseshoe, and Symbolic Dynamics
2. Robustness of Chaos
3. Statistical Properties of Chaotic Attractors
4. Structural Stability
5. Transversality, Invariant Foliation, and the Shadowing Lemma
6. Chaotic Attractors with Hyperbolic Structure
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7. Robust Chaos in Hyperbolic Systems
8. Lorenz-Type Systems
9. Robust Chaos in the Lorenz-Type Systems
10. No Robust Chaos in Quasi-Attractors
11. Robust Chaos in One-Dimensional Maps
12. Robust Chaos in 2-D Piecewise Smooth Maps
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