34,767 research outputs found
Strong statistical stability of non-uniformly expanding maps
We consider families of transformations in multidimensional Riemannian
manifolds with non-uniformly expanding behavior. We give sufficient conditions
for the continuous variation (in the -norm) of the densities of absolutely
continuous (with respect to the Lebesgue measure) invariant probability
measures for those transformations.Comment: 21 page
Gibbs-Markov structures and limit laws for partially hyperbolic attractors with mostly expanding central direction
We consider a partially hyperbolic set on a Riemannian manifold whose
tangent space splits as , for which the
centre-unstable direction expands non-uniformly on some local unstable
disk. We show that under these assumptions induces a Gibbs-Markov
structure. Moreover, the decay of the return time function can be controlled in
terms of the time typical points need to achieve some uniform expanding
behavior in the centre-unstable direction. As an application of the main result
we obtain certain rates for decay of correlations, large deviations, an almost
sure invariance principle and the validity of the Central Limit Theorem.Comment: 23 page
Random perturbations of non-uniformly expanding maps
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}.Comment: 44 pages, 2 figure
- β¦