We consider convex polygonal billiards with a reflection law that contractsthe reflection angle towards the normal. Polygonal billiards with orthogonalreflections are called slap maps. For polygons without parallel sides facingeach other, the slap map has a finite number of ergodic absolutely continuousinvariant probability measures. We show that any billiard with a stronglycontracting reflection law has the same number of ergodic SRB measures with thesame mixing periods as the ergodic absolutely continuous invariantprobabilities of its corresponding slap map. The case of billiards in regularpolygons and triangles is studied in detail.
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