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arXiv · 0810.1670

Random Chain Recurrent Sets for Random Dynamical Systems

Xiaopeng Chen·Jinqiao Duan
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Abstract

It is known by the Conley's theorem that the chain recurrent set $CR(ϕ)$ of a deterministic flow $ϕ$ 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 on noncompact separable complete metric spaces, but under a so-called \emph{absorbing condition}. In the present paper, the authors introduce a notion of random chain recurrent sets for random dynamical systems, and then prove the random Conley's theorem on noncompact separable complete metric spaces \emph{without} the absorbing condition.

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Xiaopeng Chen, Jinqiao Duan. 2009-03-26. Random Chain Recurrent Sets for Random Dynamical Systems. https://arxiv.org/abs/0810.1670

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