Global random attractors are uniquely determined by attracting deterministic compact sets |
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Authors: | Hans Crauel |
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Institution: | 1. Fachbereich 3 Mathematik, Sekr. MA 7-4, Stra?e des 17. Juni 136, 10623, Berlin, Federal Republic of Germany
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Abstract: | It is shown that for continuous dynamical systems an analogue of the Poincaré recurrence theorem holds for Ω-limit sets. A
similar result is proved for Ω-limit sets of random dynamical systems (RDS) on Polish spaces. This is used to derive that a random set which attracts every (deterministic) compact set has full measure
with respect to every invariant probability measure for theRDS. Then we show that a random attractor coincides with the Ω-limit set of a (nonrandom) compact set with probability arbitrarily
close to one, and even almost surely in case the base flow is ergodic. This is used to derive uniqueness of attractors, even
in case the base flow is not ergodic.
Entrata in Redazione il 10 marzo 1997. |
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Keywords: | Primary 58F11 58F12 Secondary 58F39 60D05 60H10 60H15 93E03 |
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