Periodic billiard orbits in right triangles
Annales de l'Institut Fourier, Volume 55 (2005) no. 1, pp. 29-46.

There is an open set of right triangles such that for each irrational triangle in this set (i) periodic billiards 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.

Il y a un ensemble ouvert de triangles rectangles tels que pour chaque triangle irrationnel dans cet ensemble : (i) les trajectoires du billard sont denses dans l'espace des phases, (ii) il y a une seule trajectoire perpendiculaire du billard, qui est non singulière, et qui n'est pas périodique, (iii) les trajectoires perpendiculaires qui sont périodiques remplissent la surface invariante correspondante.

DOI: 10.5802/aif.2088
Classification: 37C27, 37E05, 37B99
Keywords: Polygonal billiard, periodic orbits, symmetries
Troubetzkoy, Serge 1

1 Institut de mathématiques de Luminy, Centre de physique théorique, Case 907, 13288 Marseille cedex 9 (France)
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Troubetzkoy, Serge. Periodic billiard orbits in right triangles. Annales de l'Institut Fourier, Volume 55 (2005) no. 1, pp. 29-46. doi : 10.5802/aif.2088.

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