Hyperbolic polygonal billiards with finitely many ergodic SRB measures
Gianluigi Del Magno, Jo\~ao Lopes Dias, Pedro Duarte, Jos\'e Pedro, Gaiv\~ao
TL;DR
This paper investigates polygonal billiards with specific reflection laws, demonstrating that non-parallel-sided polygons have finitely many ergodic SRB measures covering almost all initial conditions.
Contribution
It proves the finiteness of ergodic SRB measures in polygonal billiards with contracting reflection laws for polygons without parallel sides facing each other.
Findings
Finitely many ergodic SRB measures exist in such billiards.
Basins of these measures cover a full Lebesgue measure set.
Results apply to polygons without parallel facing sides.
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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