Analysis of Correlation Bounds for Uniformly Expanding Maps on [0, 1]

Abstract

In this paper, we provide the decay of correlations for random dynamical systems. Precisely, we consider the uniformly C2 piecewise expanding maps defined on the unit interval satisfying λ(Tω′)=inf|Tω′|>2. As a principal tool of these studies, we use a coupling method for analyzing the coupling time of observables with bounded variation.

Keywords

• decay of correlations
• uniformly expanding maps
• random dynamical systems