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.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Lian, Zeng, "Lyapunov Exponents and Invariant Manifold for Random Dynamical Systems in a Banach Space" (2008). Theses and Dissertations. 1517.
Lyapunov exponents, multiplicative ergodic theorem, invariant manifold