Absorbing set (random dynamical systems)
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In mathematics, an absorbing set for a random dynamical system is a subset of the phase space that eventually contains the image of any bounded set under the cocycle ("flow") of the random dynamical system. As with many concepts related to random dynamical systems, it is defined in the pullback sense.
[edit] Definition
Consider a random dynamical system 
on a complete separable metric space (X,d), where the noise is chosen from a probability space 
with base flow 
. A random compact set 
is said to be absorbing if, for all bounded deterministic sets 
, there exists a (finite) random time 
such that
This is a definition in the pullback sense, as indicated by the use of the negative time shift 
.
