Escape rates and physically relevant measures for billiards with small holes

Mark Demers, Paul Wright, Lai Sang Young

Research output: Contribution to journalArticlepeer-review


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
Issue number2
StatePublished - Jan 2010

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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