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arXiv · 1312.1314

Ergodicity of polygonal slap maps

Gianluigi Del Magno·João Lopes Dias·Pedro Duarte·José Pedro Gaivão
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Abstract

Polygonal slap maps are piecewise affine expanding maps of the interval obtained by projecting the sides of a polygon along their normals onto the perimeter of the polygon. These maps arise in the study of polygonal billiards with non-specular reflections laws. We study the absolutely continuous invariant probabilities of the slap maps for several polygons, including regular polygons and triangles. We also present a general method for constructing polygons with slap maps having more than one ergodic absolutely continuous invariant probability.

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Gianluigi Del Magno, João Lopes Dias, Pedro Duarte, José Pedro Gaivão. 2013-12-04. Ergodicity of polygonal slap maps. https://doi.org/10.1088/0951-7715%2F27%2F8%2F1969

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