Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Chain Recurrent Sets for Random Dynamical Systems   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.

13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
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The categories of this paper are: econ
24
The categories of this paper are: dg-ga
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The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con