Memoirs of the American Mathematical Society 2010; 106 pp; softcover Volume: 206 ISBN10: 0821846566 ISBN13: 9780821846568 List Price: US$72 Individual Members: US$43.20 Institutional Members: US$57.60 Order Code: MEMO/206/967
 The authors 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. The authors prove a multiplicative ergodic theorem and then use this theorem to establish the stable and unstable manifold theorem for nonuniformly hyperbolic random invariant sets. Table of Contents  Introduction
 Random dynamical systems and measures of noncompactness
 Main results
 Volume function in Banach spaces
 Gap and distance between closed linear subspaces
 Lyapunov exponents and oseledets spaces
 Measurable random invariant complementary subspaces
 Proof of multiplicative ergodic theorem
 Stable and unstable manifolds
 Appendix A. Subadditive ergodic theorem
 Appendix B. Nonergodic case
 Bibliography
