Topological Dynamics of Random Dynamical Systems

Abstract

Abstract This book is devoted to the theory of topological dynamics of random dynamical systems. The theory of random dynamical systems is a relatively new and fast expanding field of research which attracts the attention of researchers from various fields of science. It unites and develops the classical deterministic theory of dynamical systems and probability theory, hence finding many applications in a very wide range of disciplines from physics to biology to engineering, finance, and economics. Recent developments call for a systematic presentation of the theory. Topological dynamics of random dynamical systems is the first book to deal with the theory of topological dynamics of random dynamical systems. It presents in detail the solutions to the most fundamental problems of topological dynamics: linearization of nonlinear smooth systems, classification, and structural stability of linear hyperbolic systems. Employing the tools and methods of algebraic ergodic theory, the theory presented in the book has surprisingly beautiful results showing the richness of random dynamical systems as well as giving a gentle generalization of the classical deterministic theory. Mathematicians working in the theory of dynamical systems, stochastic dynamics, as well as those interested in applications of mathematical systems with random noise, will find this timely book a valuable reference and rich source of modern mathematical results and methods.