Hyperbolic polygonal billiards with finitely many ergodic SRB measures

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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Veröffentlicht in:Ergodic theory and dynamical systems 2018-09, Vol.38 (6), p.2062-2085
Hauptverfasser: DEL MAGNO, GIANLUIGI, LOPES DIAS, JOÃO, DUARTE, PEDRO, GAIVÃO, JOSÉ PEDRO
Format: Artikel
Sprache:eng
Schlagworte:
Angle of reflection
Billiards
Ergodic processes
Original Article
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Zusammenfassung: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