Pathwise global attractors for stationary random dynamical systems |
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Authors: | Zdzislaw Brze?niak Marek Capiński Franco Flandoli |
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Affiliation: | (1) Institute of Mathematics, Jagiellonian University, Kraków, Poland;(2) Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56100 Pisa, Italy |
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Abstract: | Summary 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() is defined. The goal of the paper is to show that, in the case of stationary dynamical systems,A() attracts bounded sets, is measurable with respect to the -algebra of invariant sets, and is independent of 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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