Limit Theorems for Random Non-uniformly Expanding or Hyperbolic Maps with Exponential Tails

Random Perturbations of Non-Uniformly Expanding Maps

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...

Non-uniformly Expanding Dynamics in Maps with Singularities and Criticalities

We investigate a one-parameter family of interval maps arising in the study of the geometric Lorenz ow for non-classical parameter values. Our conclusion is that for all parameters in a set of positive Lebesgue measure, the map has a positive Lyapunov exponent. Furthermore, this set of parameters has a density point which plays an important dynamic role. The presence of both singular and critic...

Annealed and Quenched Limit Theorems for Random Expanding Dynamical Systems

In this paper, we investigate annealed and quenched limit theorems for random expanding dynamical systems. Making use of functional analytic techniques and more probabilistic arguments with martingales, we prove annealed versions of a central limit theorem, a large deviation principle, a local limit theorem, and an almost sure central limit theorem. We also discuss the quenched central limit th...

2 00 6 Large Deviations for Non - Uniformly Expanding Maps

We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hy-perbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space average with respect to a physical measure and compare this with the time averages along orbits of the map, showing that the Lebesgue measure of the set of...