Almost sure mixing rates for non-uniformly expanding maps

Almost Sure Rates of Mixing for I.i.d. Unimodal Maps

Mixing and Decay of Correlations in Non-uniformly Expanding Maps

I discuss recent results on decay of correlations for nonuniformly expanding maps. Throughout the discussion, I address the question of why different dynamical systems have different rates of decay of correlations and how this may reflect underlying geometrical characteristics of the system.

Almost Sure Invariance Principle for Random Piecewise Expanding Maps

The objective of this note is to prove the almost sure invariance principle (ASIP) for a large class of random dynamical systems. The random dynamics is driven by an invertiblemeasure preserving transformation σ of (Ω,F ,P) called the base transformation. Trajectories in the phase space X are formed by concatenations f ω := fσn−1ω ◦ · · · ◦ fσω ◦ fω of maps from a family of maps fω : X → X, ω ∈...

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...