Absolutely continuous invariant measures for random non-uniformly expanding maps

Random Perturbations of Non-Uniformly Expanding Maps

Regularity of Absolutely Continuous Invariant Measures for Piecewise Expanding Unimodal Maps

Let f : [0, 1]→ [0, 1] be a piecewise expanding unimodal map of class C, with k ≥ 1, and μ = ρdx the (unique) SRB measure associated to it. We study the regularity of ρ. In particular, points N where ρ is not differentiable has zero Hausdorff dimension, but is uncountable if the critical orbit of f is dense. This improves on a work of Szewc (1984). We also obtain results about higher order diff...

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...

Absolutely continuous invariant measures for piecewise real-analytic expanding maps on the plane

We prove the existence of absolutely continuous invariant measures for piecewise real-analytic expanding maps on bounded regions in the plane.

A Generalization of Straube’s Theorem: Existence of Absolutely Continuous Invariant Measures for Random Maps

A randommap is a discrete-time dynamical system in which one of a number of transformations is randomly selected and applied at each iteration of the process. In this paper, we study randommaps. The main result provides a necessary and sufficient condition for the existence of absolutely continuous invariant measure for a randommap with constant probabilities and position-dependent probabilities.