2008/10/09 by Xiaopeng Chen, Chen, Xiaopeng, Jinqiao Duan +1
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #37B20 #37B25 #37B35 #37H99 #Caveolin-1 and cellular processes #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stability and Controllability of Differential Equations #math.DS #msc:37B20 #msc:37B25 #msc:37B35 #msc:37H99
paper · pdf · doi:10.48550/arxiv.0810.1670
14 pages
openalex publication_date 2008/10/09 · arxiv created 2009/03/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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 without the absorbing condition.