Sasha Skripchenko – Polygonal billiards with 1-sided scattering

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Date(s) - 4 octobre 2013

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We study polygonal billiards with one-sided vertical mirror scattered on a square billiard table. We associate trajectories of these kinds of billiards with a particular case of interval translation mappings called double rotations, and study orbit behavior and questions of ergodicity and unique ergodicity. Our main result is a linear estimate on the complexity of billiard trajectories in case of rational positions of the mirror.This result also generalizes to certain other rational polygons with one sided scatterers located at an axis of symmetry. (joint work with Serge Troubetzkoy)