Periodic billiard orbits are dense in rational polygons

Boshernitzan, M.; Galperin, G.; Krüger, T.; Troubetzkoy, S.

doi:10.1090/S0002-9947-98-02089-3

Periodic billiard orbits are dense in rational polygons
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by M. Boshernitzan, G. Galperin, T. Krüger and S. Troubetzkoy PDF

Trans. Amer. Math. Soc. 350 (1998), 3523-3535 Request permission

Abstract:

We show that periodic orbits are dense in the phase space for billiards in polygons for which the angle between each pair of sides is a rational multiple of $\pi .$

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