Hyperbolic polygonal billiards with finitely many ergodic SRB measures

2015/07/22 by Gianluigi Del Magno, Del Magno, Gianluigi, João Lopes Dias +5
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1507.06250

26 pages, 2 figures

arxiv created 2015/07/22 · arxiv updated 2015/07/23

Abstract

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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