Mathematical Research Letters
Volume 20 (2013)
Memory loss for time-dependent piecewise expanding systems in higher dimension
Pages: 141 – 161
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.
Hilbert metric, memory loss, mixing, piecewise expanding maps, timedependent dynamical systems
2010 Mathematics Subject Classification
37C60, 37D20, 37D50, 82Cxx