Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Synchronisation of almost all trajectories of a random dynamical system   It has been shown by Le Jan that, given a memoryless-noise random dynamical
system together with an ergodic distribution for the associated Markov
transition probabilities, if the support of the ergodic distribution admits
locally asymptotically stable trajectories, then there is a random attracting
set consisting of finitely many points, whose basin of forward-time attraction
includes a random full measure open set. In this paper, we present necessary
and sufficient conditions for this attracting set to be a singleton; our result
does not require the state space to be compact, but holds on general Lusin
metric spaces.

10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an