Luchezar Stoyanov
Published 2009-11-26, updated 2010-10-28Version 4
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.
On a structure of non-wandering set of an $Ω$-stable 3-diffeomorphism possessing a hyperbolic attractor
A note on the hyperbolicity of the non-wandering sets of real quadratic maps
Streams and Graphs of Dynamical Systems
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