Dispersing billiards with moving scatterers
Dynamical Systems
2015-06-11 v4 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1210.0011,
title = {Dispersing billiards with moving scatterers},
author = {Mikko Stenlund and Lai-Sang Young and Hongkun Zhang},
journal= {arXiv preprint arXiv:1210.0011},
year = {2015}
}
Comments
39 pages, 3 figures. (Minor improvements/corrections in this version; to appear in Communications in Mathematical Physics.)