Random Dynamical Systems

This book is the first systematic presentation of the theory of dynamicalsystems under the influence of randomness. It includes products of randommappings as we... » 

This book is the first systematic presentation of the theory of dynamicalsystems under the influence of randomness. It includes products of randommappings as well as random and stochastic differential equations. The basicmulitplicative ergodic theorem is presented and provides a random substitutefor linear algebra. On its basis random invariant manifolds are constructedsystems are simplified by smooth random coordinate transformations randomnormal forms and qualitative changes in families of random systems randombifurcation theory are studied. Numerous instructive examples are treatedanalytically or numerically. The main intention however is to present areliable and rather complete source of reference which lays the foundation forfuture work and applications. TOCI. Random Dynamical Systems and TheirGenerators Basic Definitions. Invariant Measures. Generation. II.Multiplicative Ergodic Theoryin Euclidean Space on Bundlesfor Rela tedLinear Random Dynamical Systems Random Dynamcial Systems on HomogeneousSpaces. III. Smooth Random Dynamical Systems Invariant Manifolds NormalForms Bifurcation Theory. IV. Appendices Measurable Systems Smooth DynamicalSystems. «