Repellers for non-uniformly expanding maps with singular or critical points

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...

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...

Phase Transitions for Uniformly Expanding Maps

Given a uniformly expanding map of two intervals we describe a large class of potentials admitting unique equilibrium measures. This class includes all Hölder continuous potentials but goes far beyond them. We also construct a family of continuous but not Hölder continuous potentials for which we observe phase transitions. This provides a version of the example in [9] for uniformly expanding maps.