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Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space. (English) Zbl 1200.37047

Mem. Am. Math. Soc. 967, v, 106 p. (2010).
The authors study Lyapunov exponents and associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space. First, a multiplicative ergodic theorem is proved. Then, it is used to establish the existence of stable and unstable manifolds of Pesin type for nonuniformly hyperbolic random invariant sets.

MSC:

37H15 Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents
37A30 Ergodic theorems, spectral theory, Markov operators
37L55 Infinite-dimensional random dynamical systems; stochastic equations
47A35 Ergodic theory of linear operators

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