Escape rates and physically relevant measures for billiards with small holesCommunications in Mathematics Physics
AbstractWe 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.
Published CitationMark 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.
Citation InformationMark 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/