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Topological transitivity of billiards in polygons

A. N. Zemlyakov^a, A. B. Katok<sup>b

a</sup> M. V. Lomonosov Moscow State University
^b Central Economics and Mathematics Institute, USSR Academy of Sciences

Abstract: Consider a billiard in a polygon $Q\subset R^2$ having all angles commensurate with $\pi$. 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.

UDC: 513.83

Received: 26.09.1974

 English version: Mathematical Notes, 1975, 18:2, 760–764

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