Dynamical chaos and hyperbolic attractors: from mathematics to physics

The book considers possibilities of occurrence of physical systems generating structurally stable chaos due to the presence of uniformly hyperbolic attractors, such as Smale-Williams solenoid, DA-attractor of Smale, attractors of Plykin type. An overview of the content of the hyperbolic theory is given, as well as a review of possible situations of appearance of hyperbolic attractors. Based on the physical principles, examples of systems with hyperbolic chaotic attractors are constructed. Several methods for computer validation of the hyperbolicity are considered and illustrated by application to concrete systems. Modeling of electronic devices with hyperbolic attractors is discussed, and results concerning observation of hyperbolic chaos in laboratory experiments are summarized. The book is intended for students, post-graduate students, and researchers, working or interested in the field of nonlinear dynamics and its applications.