Hyperbolic polygonal billiards with finitely many ergodic SRB measures

We study polygonal billiards with reflection laws contracting the angle of reflection towards the normal. It is shown that if a polygon does not have parallel sides facing each other, then the corresponding billiard map has finitely many ergodic Sinai–Ruelle–Bowen measures whose basins cover a set o...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2018-09, Vol.38 (6), p.2062-2085
Main Authors: DEL MAGNO, GIANLUIGI, LOPES DIAS, JOÃO, DUARTE, PEDRO, GAIVÃO, JOSÉ PEDRO
Format: Article
Language:English
Subjects:
Angle of reflection
Billiards
Ergodic processes
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Summary:We study polygonal billiards with reflection laws contracting the angle of reflection towards the normal. It is shown that if a polygon does not have parallel sides facing each other, then the corresponding billiard map has finitely many ergodic Sinai–Ruelle–Bowen measures whose basins cover a set of full Lebesgue measure.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2016.119