An expansion estimate for dispersing planar billiards with corner points

It is known that the dynamics of planar billiards satisfies strong mixing properties (e.g. exponential decay of correlations) provided that some expansion condition on unstable curves is satisfied. This condition has been shown to always hold for smooth dispersing planar billiards, but it needed to...

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Bibliographic Details
Main Authors De Simoi, Jacopo, Tóth, Imre Péter
Format Journal Article
LanguageEnglish
Published 31.12.2012
Subjects
Mathematics - Dynamical Systems
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Summary:It is known that the dynamics of planar billiards satisfies strong mixing properties (e.g. exponential decay of correlations) provided that some expansion condition on unstable curves is satisfied. This condition has been shown to always hold for smooth dispersing planar billiards, but it needed to be assumed separately in the case of dispersing planar billiards with corner points. We prove that this expansion condition holds for any dispersing planar billiard with corner points, no cusps and bounded horizon.
DOI:10.48550/arxiv.1212.6897