Dolgopyat type estimates for pinched open billiard flows (Revised)
Dynamical Systems
2010-10-29 v4 Spectral Theory
Abstract
In this paper we consider open billiard flows in Euclidean spaces with C^1 (un)stable laminations over their non-wandering sets. We show that for such billiard flows the standard symplectic form satisfies a specific non-degeneracy condition over the non-wandering set. This allows to use some previous general results and obtain Dolgopyat type estimates for spectra of Ruelle transfer operators under simpler conditions. We also describe a class of open billiard flows in Euclidean spaces satisfying a certain pinching condition, which in turn implies that the (un)stable laminations over the non-wandering set are C^1.
Keywords
Cite
@article{arxiv.0911.5000,
title = {Dolgopyat type estimates for pinched open billiard flows (Revised)},
author = {Luchezar Stoyanov},
journal= {arXiv preprint arXiv:0911.5000},
year = {2010}
}