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. The book 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 experiences for both readers and researchers in nonlinear science in general, and chaos theory in particular.
Sample Chapter(s)
Chapter 1: Poincaré Map Technique, Smale Horseshoe, and Symbolic Dynamics (613 KB)
Contents:
- Poincaré Map Technique, Smale Horseshoe, and Symbolic Dynamics
- Robustness of Chaos
- Statistical Properties of Chaotic Attractors
- Structural Stability
- Transversality, Invariant Foliation, and the Shadowing Lemma
- Chaotic Attractors with Hyperbolic Structure
- Robust Chaos in Hyperbolic Systems
- Lorenz-Type Systems
- Robust Chaos in the Lorenz-Type Systems
- No Robust Chaos in Quasi-Attractors
- Robust Chaos in One-Dimensional Maps
- Robust Chaos in 2-D Piecewise Smooth Maps
Readership: Advanced undergraduate and graduate students, researchers, engineers and instructors interested in chaos and dynamical systems.
