Physical Sciences and Mathematics Commons^™

Lyapunov Exponents And Invariant Manifold For Random Dynamical Systems In A Banach Space, Zeng Lian

Theses and Dissertations

We study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. We prove a multiplicative ergodic theorem. Then, we use this theorem to establish the stable and unstable manifold theorem for nonuniformly hyperbolic random invariant sets.