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Billiards in Polygons
Carlo Boldrighini, Michael Keane and Federico Marchetti
The Annals of Probability
Vol. 6, No. 4 (Aug., 1978), pp. 532-540
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2243120
Page Count: 9
You can always find the topics here!Topics: Polygons, Vertices, Billiards, Ergodic theory, Dynamical systems, Triangles, Mathematics, Entropy, Periodic orbits, Semigroups
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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.
The Annals of Probability © 1978 Institute of Mathematical Statistics