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

Chinmaya Gupta (Department of Mathematics, University of Houston, Texas, U.S.A.)

William Ott (Department of Mathematics, University of Houston, Texas, U.S.A.)

Andrei Török (Department of Mathematics, University of Houston, Texas, U.S.A.)

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

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