Memory loss for time-dependent dynamical systems

TL;DR

This paper proves exponential memory loss in certain time-dependent dynamical systems, specifically for expanding maps and one-dimensional piecewise expanding maps with slowly changing parameters, advancing understanding of their long-term behavior.

Contribution

It establishes exponential loss of memory for specific classes of time-dependent dynamical systems, a novel result for systems with slowly varying parameters.

Findings

Exponential memory loss for expanding maps

Memory decay in one-dimensional piecewise expanding maps

Applicable to systems with slowly changing parameters

Abstract

This paper discusses the evolution of probability distributions for certain time-dependent dynamical systems. Exponential loss of memory is proved for expanding maps and for one-dimensional piecewise expanding maps with slowly varying parameters.