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	Oliver Tearne: Collapse of attractors under small random perturbations
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Crauel and Flandoli show that the random attractor corresponding
to a one-dimensional random dynamical system (RDS) is a one point
set, provided there exists a compact absorbing set and a unique
invariant Markov measure. For example, adding arbitrarily small
additive white noise to the one-dimensional ODE $\dot{x}=x-x^3$
causes the deterministic attractor to collapse from an interval to
a single point.
I will present an algorithm used to investigate this phenomenon in
two dimensions, and analytical results showing the random

attractor is a one point set for $n$-dimensional RDS generated by
a class of gradient stochastic differential equations. Central to
the algorithm is the result

$\partial\Omega_B\subseteq\Omega_{\partial B}$ for omega-limit
sets of compact sets $B$.  This is used to prove that boundaries
of deterministic and random attractors are covered by omega-limit

sets of boundaries of compact absorbing sets.  To apply the
algorithm I will show that any neighbourhood of an absorbing set
for the deterministic system is also absorbing for the
corresponding stochastic system with positive probability.
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