Abstract
Consider a billiard in a polygon Q⊂R2 having all angles commensurate with π. For the majority of initial directions, density of every infinite semitrajectory in configuration space is proved. Also proved is the typicality of polygons for which some billiard trajectory is dense in phase space.
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Ya. G. Sinai, Introduction to Ergodic Theory [in Russian], Erevan University Press, Erevan (1973).
A. G. Maier, “Trajectories on orientable surfaces,” Matem. Sbornik,12 (54), No. 1, 71–84 (1943).
A. B. Katok, “Invariant measures of flows on orientable surfaces,” Dokl. Akad. Nauk SSSR,211, No. 4, 775–778 (1973).
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Translated from Matematicheskie Zametki, Vol. 18, No. 2, pp. 291–300, August, 1975.
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Zemlyakov, A.N., Katok, A.B. Topological transitivity of billiards in polygons. Mathematical Notes of the Academy of Sciences of the USSR 18, 760–764 (1975). https://doi.org/10.1007/BF01818045
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DOI: https://doi.org/10.1007/BF01818045