Geodesic
Topological transitivity of billiards in polygons
Matematičeskie zametki, Tome 18 (1975) no. 2, pp. 291-300.

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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. 
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     author = {A. N. Zemlyakov and A. B. Katok},
     title = {Topological transitivity of billiards in polygons},
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A. N. Zemlyakov; A. B. Katok. Topological transitivity of billiards in polygons. Matematičeskie zametki, Tome 18 (1975) no. 2, pp. 291-300. http://geodesic.mathdoc.fr/item/MZM_1975_18_2_a14/