Ergodicity of polygonal slap maps
Dynamical Systems
2015-06-18 v1
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.
Keywords
Cite
@article{arxiv.1312.1314,
title = {Ergodicity of polygonal slap maps},
author = {Gianluigi Del Magno and João Lopes Dias and Pedro Duarte and José Pedro Gaivão},
journal= {arXiv preprint arXiv:1312.1314},
year = {2015}
}
Comments
17 pages, 6 figures