Billiards in rational polygons: Periodic trajectories, symmetries and $d$-stability

Ya. B. Vorobets

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 517.938

Received: 18.02.1997

DOI: 10.4213/mzm1588

 English version: Mathematical Notes, 1997, 62:1, 56–63

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