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arXiv · 2008.05389

Bridge to Hyperbolic Polygonal Billiards

Hassan Attarchi·Leonid A. Bunimovich
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Abstract

It is well-known that billiards in polygons cannot be chaotic (hyperbolic). Particularly Kolmogorov-Sinai entropy of any polygonal billiard is zero. We consider physical polygonal billiards where a moving particle is a hard disc rather than a point (mathematical) particle and show that typical physical polygonal billiard is hyperbolic at least on a subset of positive measure and therefore has a positive Kolmogorov- Sinai entropy for any positive radius of the moving particle (provided that the particle is not so big that it cannot move within a polygon). This happens because a typical physical polygonal billiard is equivalent to a mathematical (point particle) semi-dispersing billiard. We also conjecture that in fact typical physical billiard in polygon is ergodic under the same conditions.

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Hassan Attarchi, Leonid A. Bunimovich. 2020-08-12. Bridge to Hyperbolic Polygonal Billiards. https://arxiv.org/abs/2008.05389

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