Hyperbolic polygonal billiards with finitely many ergodic SRB measures

摘要

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.