Frontiers in Mathematical Sciences

Exponential Memory Loss for Piecewise Expanding Maps of Metric Spaces

Peyman Eslami
University of Warwick


I will briefly discuss work in progress on studying the exponential memory loss for piecewise expanding $C^{1+}$ maps with countably many branches on metric spaces. I will mostly discuss the sufficient conditions for proving such a result including the conditions on the complexity growth of the partition elements. We will not assume or use the existence of a Markov structure for such dynamical systems and give explicit estimates on the constants involved in the exponential decay.