Hyperbolic polygonal billiards with finitely many ergodic SRB measures

Gianluigi Del Magno; Jo\~ao Lopes Dias; Jos\'e Pedro Gaiv\~ao; Pedro Duarte

arxiv: 1507.06250 · v1 · pith:V5FINXEQnew · submitted 2015-07-22 · 🧮 math.DS

Hyperbolic polygonal billiards with finitely many ergodic SRB measures

Gianluigi Del Magno , Jo\~ao Lopes Dias , Pedro Duarte , Jos\'e Pedro Gaiv\~ao This is my paper

classification 🧮 math.DS

keywords billiardsergodicfinitelymanymeasurespolygonalanglebasins

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We study polygonal billiards with reflection laws contracting the reflected angle 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 SRB measures whose basins cover a set of full Lebesgue measure.

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Hyperbolic polygonal billiards with finitely many ergodic SRB measures

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