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Article
Escape rates and physically relevant measures for billiards with small holes
Communications in Mathematics Physics
  • Mark Demers, Fairfield University
  • Paul Wright
  • Lai-Sang Young
Document Type
Article
Article Version
Post-print
Publication Date
1-1-2010
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.
Comments

Copyright 2010 Springer-Verlag

Published Citation
Mark Demers, Paul Wright and Lai-Sang Young, "Escape rates and physically relevant measures for billiards with small holes," Communications in Mathematical Physics 294: 2 (2010), 353-388.
DOI
10.1007/s00220-009-0941-y
None
Peer Reviewed
Citation Information
Mark Demers, Paul Wright and Lai-Sang Young. "Escape rates and physically relevant measures for billiards with small holes" Communications in Mathematics Physics Vol. 294 Iss. 2 (2010)
Available at: http://works.bepress.com/mark_demers/8/