Dolgopyat type estimates for pinched open billiard flows (Revised)

Details Dolgopyat type estimates for pinched open billiard flows (Revised) Dolgopyat type estimates for pinched open billiard flows (Revised)

2009-11-26

arxiv.org/abs/0911.5000v4

Mathematics

Dynamical Systems

Scientific paper

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.

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