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https://hdl.handle.net/2440/66776
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Type: | Journal article |
Title: | Random chain recurrent sets for random dynamical systems |
Author: | Chen, X. Duan, J. |
Citation: | Dynamics and Stability of Systems, 2009; 24(4):537-546 |
Publisher: | Taylor & Francis Ltd |
Issue Date: | 2009 |
ISSN: | 1468-9367 1468-9375 |
Statement of Responsibility: | Xiaopeng Chen and Jinqiao Duana |
Abstract: | It is known by the Conley’s theorem that the chain recurrent set CR(’) of a deterministic flow’ on a compact metric space is the complement of the union of sets B(A) A, where A varies over the collection of attractors and B(A) is the basin of attraction of A. It has recently been shown that a similar decomposition result holds for random dynamical systems (RDSs) on non-compact separable complete metric spaces, but under a so-called absorbing condition. In the present article, the authors introduce a notion of random chain recurrent sets for RDSs, and then prove the random Conley’s theorem on non-compact separable complete metric spaces without the absorbing condition. |
Keywords: | chain recurrent sets attractors Conley’s theorem random dynamical systems cocycle |
Rights: | (c) 2009 Taylor & Francis |
DOI: | 10.1080/14689360903164173 |
Published version: | http://dx.doi.org/10.1080/14689360903164173 |
Appears in Collections: | Aurora harvest Mathematical Sciences publications |
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