Non-integrability of open billiard flows and Dolgopyat-type estimates
type: Item
instance of: scholarly article
title: Non-integrability of open billiard flows and Dolgopyat-type estimates
zbMATH Open document ID: 1323.37017
DOI: 10.1017/S0143385710000933
published in: Ergodic Theory and Dynamical Systems
publication date: 2012-05-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/0911.5000
Mathematics Subject Classification ID: 37C30
Mathematics Subject Classification ID: 37D50
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 37J30
zbMATH DE Number: 6038238
zbMATH Keywords: open billiard flows
zbMATH Keywords: symplectic form
zbMATH Keywords: non-integrability
author: Luchezar Stoyanov
MaRDI profile type: Publication
arXiv ID: 0911.5000
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review text: For an open billiard flow in \(\mathbb R^n\), the author shows that the standard symplectic form \(d\alpha\) in \(\mathbb R^n\) satisfies a specific non-integrability condition over its non-wandering set \(\Lambda\). This together with the author's other new results provide Dolgopyat-type estimates for the spectra of Ruelle transfer operators under simpler conditions. The author also describes a class of open billiard flows in \(\mathbb R^n\), \(n\geq 3\), satisfying a certain pinching condition, which in turn implies that the (un)stable laminations over the non-wandering set are \(C^1\).
reviewed by: Xiang Zhang
description: scientific article; zbMATH DE number 6038238