Bridge to Hyperbolic Polygonal Billiards
From MaRDI portal
Publication:4992240
zbMATH Open1471.37033arXiv2008.05389MaRDI QIDQ4992240
Hassan Attarchi, L. A. Bunimovich
Publication date: 7 June 2021
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.
Full work available at URL: https://arxiv.org/abs/2008.05389
Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Dynamical systems with hyperbolic orbits and sets (37D05) Dynamical systems with singularities (billiards, etc.) (37C83)
This page was built for publication: Bridge to Hyperbolic Polygonal Billiards
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q4992240)
