Dispersing Billiards with Moving Scatterers

Mikko Stenlund, Lai-Sang Young, Hongkun Zhang

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)909-955
Number of pages47
JournalCommunications in Mathematical Physics
Volume322
Issue number3
DOIs
StatePublished - Sep 2013

Fingerprint

dispersing
Billiards
scattering
dynamical systems
Statistical property
Collision
Dynamical system
collisions
Model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Dispersing Billiards with Moving Scatterers. / Stenlund, Mikko; Young, Lai-Sang; Zhang, Hongkun.

In: Communications in Mathematical Physics, Vol. 322, No. 3, 09.2013, p. 909-955.

Research output: Contribution to journalArticle

Stenlund, Mikko ; Young, Lai-Sang ; Zhang, Hongkun. / Dispersing Billiards with Moving Scatterers. In: Communications in Mathematical Physics. 2013 ; Vol. 322, No. 3. pp. 909-955.
@article{9bbf3a7142f54b24be6165e42d2bdb30,
title = "Dispersing Billiards with Moving Scatterers",
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.",
author = "Mikko Stenlund and Lai-Sang Young and Hongkun Zhang",
year = "2013",
month = "9",
doi = "10.1007/s00220-013-1746-6",
language = "English (US)",
volume = "322",
pages = "909--955",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer New York",
number = "3",

}

TY - JOUR

T1 - Dispersing Billiards with Moving Scatterers

AU - Stenlund, Mikko

AU - Young, Lai-Sang

AU - Zhang, Hongkun

PY - 2013/9

Y1 - 2013/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84880507464&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880507464&partnerID=8YFLogxK

U2 - 10.1007/s00220-013-1746-6

DO - 10.1007/s00220-013-1746-6

M3 - Article

AN - SCOPUS:84880507464

VL - 322

SP - 909

EP - 955

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -