Random Chain Recurrent Sets for Random Dynamical Systems

Details Random Chain Recurrent Sets for Random Dynamical Systems Random Chain Recurrent Sets for Random Dynamical Systems

2008-10-09

arxiv.org/abs/0810.1670v2

Mathematics

Dynamical Systems

14 pages

Scientific paper

It is known by the Conley's theorem that the chain recurrent set $CR(\phi)$ of a deterministic flow $\phi$ 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.

Affiliated with

Also associated with

No associations

Rating

Random Chain Recurrent Sets for Random Dynamical Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Random Chain Recurrent Sets for Random Dynamical Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random Chain Recurrent Sets for Random Dynamical Systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-461095