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August, 1978 Billiards in Polygons
Carlo Boldrighini, Michael Keane, Federico Marchetti
Ann. Probab. 6(4): 532-540 (August, 1978). DOI: 10.1214/aop/1176995475

Abstract

Some questions concerning the orbits of a billiard ball in a polygon are studied. It is shown that almost all such orbits come arbitrarily close to a vertex of the polygon, implying that the entropy of the corresponding geodesic flow is zero. For polygons with rational angles, we show by using interval exchange transformations that almost all orbits are spatially dense. Two applications are given.

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Carlo Boldrighini. Michael Keane. Federico Marchetti. "Billiards in Polygons." Ann. Probab. 6 (4) 532 - 540, August, 1978. https://doi.org/10.1214/aop/1176995475

Information

Published: August, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0377.28014
MathSciNet: MR644840
Digital Object Identifier: 10.1214/aop/1176995475

Subjects:
Primary: 28A65
Secondary: 54H20‎

Keywords: interval exchange transformations , Polygonal billiards

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 4 • August, 1978
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