Escape rates and physically relevant measures for billiards with small holes

Mark Demers, Paul Wright, Lai-Sang Young

Research output: Contribution to journalArticle

Abstract

We study the billiard map corresponding to a periodic Lorentz gas in 2-dimensions in the presence of small holes in the table. We allow holes in the form of open sets away from the scatterers as well as segments on the boundaries of the scatterers. For a large class of smooth initial distributions, we establish the existence of a common escape rate and normalized limiting distribution. This limiting distribution is conditionally invariant and is the natural analogue of the SRB measure of a closed system. Finally, we prove that as the size of the hole tends to zero, the limiting distribution converges to the smooth invariant measure of the billiard map.

Original languageEnglish (US)
Pages (from-to)353-388
Number of pages36
JournalCommunications in Mathematical Physics
Volume294
Issue number2
DOIs
StatePublished - Jan 2010

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Escape Rate
Billiards
Limiting Distribution
escape
SRB Measure
Lorentz Gas
Space Shuttle Boosters
Lorentz gas
Open set
Invariant Measure
Table
scattering
Tend
Analogue
Converge
Closed
Invariant
Zero
analogs

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Escape rates and physically relevant measures for billiards with small holes. / Demers, Mark; Wright, Paul; Young, Lai-Sang.

In: Communications in Mathematical Physics, Vol. 294, No. 2, 01.2010, p. 353-388.

Research output: Contribution to journalArticle

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