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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 suchbilliard flows the standard symplectic form satisfies a specific non-degeneracycondition over the non-wandering set. This allows to use some previous generalresults and obtain Dolgopyat type estimates for spectra of Ruelle transferoperators under simpler conditions. We also describe a class of open billiardflows in Euclidean spaces satisfying a certain pinching condition, which inturn implies that the (un)stable laminations over the non-wandering set areC^1.

Dolgopyat type estimates for pinched open billiard flows (Revised)