Escape rates and physically relevant measures for billiards with small holes

Authors

Mark Demers, Fairfield UniversityFollow
Paul Wright
Lai-Sang Young

Document Type

Article

Article Version

Post-print

Publication Date

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

Publication Title

Communications in Mathematics Physics

Repository Citation

Demers, Mark; Wright, Paul; and Young, Lai-Sang, "Escape rates and physically relevant measures for billiards with small holes" (2010). Mathematics Faculty Publications. 43.
https://digitalcommons.fairfield.edu/mathandcomputerscience-facultypubs/43

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

Peer Reviewed