Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space - Lian, Zeng; Lu, Kening (Memoirs of the American Mathematical Society, 2010)
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.