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# Mathematical Research Letters

## Volume 20 (2013)

### Number 1

### Memory loss for time-dependent piecewise expanding systems in higher dimension

Pages: 141 – 161

DOI: http://dx.doi.org/10.4310/MRL.2013.v20.n1.a12

#### Authors

#### Abstract

We prove a counterpart of exponential decay of correlations for certain nonstationary systems. Namely, given two probability measures absolutely continuous with respect to a reference measure, their quasi-Hölder distance (and in particular their $L^1$ distance) decreases exponentially under action by compositions of arbitrarily chosen maps close to those that are both piecewise expanding and mixing in a certain sense.

#### Keywords

Hilbert metric, memory loss, mixing, piecewise expanding maps, timedependent dynamical systems

#### 2010 Mathematics Subject Classification

37C60, 37D20, 37D50, 82Cxx

Published 20 September 2013