Dispersing billiards with moving scatterers

TL;DR

This paper introduces a model of Sinai billiards with moving scatterers, demonstrating exponential loss of memory and providing insights into the statistical properties of time-dependent dynamical systems.

Contribution

It presents a novel model of billiards with moving scatterers and proves exponential memory loss using a coupling argument, advancing understanding of non-stationary dynamical systems.

Findings

Exponential loss of memory at uniform rates.

Coupling argument applicable to non-stationary billiard maps.

Framework for statistical analysis of time-dependent systems.

Abstract

We propose a model of Sinai billiards with moving scatterers, in which the locations and shapes of the scatterers may change by small amounts between collisions. Our main result is the exponential loss of memory of initial data at uniform rates, and our proof consists of a coupling argument for non-stationary compositions of maps similar to classical billiard maps. This can be seen as a prototypical result on the statistical properties of time-dependent dynamical systems.