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Non-integrability of open billiard flows and Dolgopyat-type estimates

Published online by Cambridge University Press:  05 April 2011

LUCHEZAR STOYANOV
LUCHEZAR STOYANOV*
Affiliation:
University of Western Australia, Crawley, WA 6009, Australia (email: stoyanov@maths.uwa.edu.au)
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Abstract

We consider open billiard flows in ℝn and show that the standard symplectic form dα in ℝn satisfies a specific non-integrability condition over their non-wandering sets Λ. This allows one to use the main result in Stoyanov [Spectra of Ruelle transfer operators for Axiom A flows. Preprint, 2010, arXiv:0810.1126v4 [math.DS]] and obtain Dolgopyat-type estimates for the spectra of Ruelle transfer operators under simpler conditions. We also describe a class of open billiard flows in ℝn(n≥3) satisfying a certain pinching condition, which in turn implies that the (un)stable laminations over the non-wandering set are C1.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 1 , February 2012 , pp. 295 - 313
Copyright
Copyright © Cambridge University Press 2011

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