- 00-461 Jose F. Alves, Vitor Araujo
- Random perturbations of non-uniformly expanding
maps
(460K, postscript)
Nov 21, 00
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Abstract. We give both sufficient conditions and
necessary conditions for the stochastic stability of
non-uniformly expanding maps either with or without
critical sets. We also show that the number of probability
measures describing the statistical asymptotic behaviour of
random orbits is bounded by the number of SRB measures if
the noise level is small enough.
As an application
of these results we prove the stochastic stability of certain
classes of non-uniformly expanding maps introduced in
\cite{V} and \cite{ABV}.
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