Geodesic
Billiards in rational polygons: Periodic trajectories, symmetries and $d$-stability
Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 66-75

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Periodic trajectories of billiards in rational polygons satisfying the Veech alternative, in particular, in right triangles with an acute angle of the form $\pi/n$ with integer $n$ are considered. The properties under investigation include: symmetry of periodic trajectories, asymptotics of the number of trajectories whose length does not exceed a certain value, stability of periodic billiard trajectories under small deformations of the polygon. 
@article{MZM_1997_62_1_a6,
     author = {Ya. B. Vorobets},
     title = {Billiards in rational polygons: {Periodic} trajectories, symmetries and $d$-stability},
     journal = {Matemati\v{c}eskie zametki},
     pages = {66--75},
     publisher = {mathdoc},
     volume = {62},
     number = {1},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a6/}
}
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Ya. B. Vorobets. Billiards in rational polygons: Periodic trajectories, symmetries and $d$-stability. Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 66-75. http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a6/