Random Dynamic Systems

This book is the first systematic presentation of the theory of random dynamical systems, which refers to dynamical systems influenced by some form of randomness. The theory includes products of random mappings as well as random and stochastic differential equations. The author's approach is based on Oseledets' multiplicative ergodic theorem for linear random systems, for which a detailed proof is provided. This theorem offers a random substitute for linear algebra and can serve as the foundation for a local theory of nonlinear random systems. In particular, global and local random invariant manifolds are constructed, and their regularity is demonstrated. Techniques for simplifying a system through random continuous or smooth coordinate transformations are developed, including the random Hartman-Grobman theorem and random normal forms. The book also addresses qualitative changes in families of random systems, specifically random bifurcation.