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Zbl 1063.37022
Troubetzkoy, Serge
Periodic billiard orbits in right triangles. (English)
[J] Ann. Inst. Fourier 55, No. 1, 29-46 (2005). ISSN 0373-0956; ISSN 1777-5310/e

Summary: There is an open set of right triangles such that for each irrational triangle in this set (i) periodic billiard orbits are dense in the phase space, (ii) there is a unique nonsingular perpendicular billiard orbit which is not periodic, and (iii) the perpendicular periodic orbits fill the corresponding invariant surface.

MSC 2000:: *37C27 Periodic orbits of vector fields and flows
37E05 Maps of the interval
37B99 Topological dynamics
37D50 Hyperbolic systems with singularities

Keywords: Polygonal billiard; periodic orbits; symmetries

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