Abstract
The asymptotic behaviour of random dynamical systems in Polish spaces is considered. Under the assumption of existence of a random compact absorbing set, assumption supposed to hold path by path, a candidate pathwise attractorA(ω) is defined. The goal of the paper is to show that, in the case of stationary dynamical systems,A(ω) attracts bounded sets, is measurable with respect to the σ-algebra of invariant sets, and is independent of ω when the system is ergodic. An application to a general class of Navier-Stokes type equations perturbed by a multiplicative ergodic real noise is discussed in detail.
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