Contents Online
Mathematical Research Letters
Volume 20 (2013)
Number 1
Memory loss for time-dependent piecewise expanding systems in higher dimension
Pages: 141 – 161
DOI: https://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