no. 1
Periodic billiard orbits in right triangles  [ Trajectoires périodiques du billard dans un triangle rectangle ]
Annales de l'Institut Fourier, Tome 55 (2005) no. 1, pp. 29-46.

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.

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.

DOI : https://doi.org/10.5802/aif.2088
Classification : 37C27,  37E05,  37B99
Mots clés : billiard polygonal, trajectoire périodique, symétries 
@article{AIF_2005__55_1_29_0,
     author = {Troubetzkoy, Serge},
     title = {Periodic billiard orbits in right triangles},
     journal = {Annales de l'Institut Fourier},
     pages = {29--46},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {55},
     number = {1},
     year = {2005},
     doi = {10.5802/aif.2088},
     zbl = {1063.37022},
     mrnumber = {2141287},
     language = {en},
     url = {archive.numdam.org/item/AIF_2005__55_1_29_0/}
}
Troubetzkoy, Serge. Periodic billiard orbits in right triangles. Annales de l'Institut Fourier, Tome 55 (2005) no. 1, pp. 29-46. doi : 10.5802/aif.2088. http://archive.numdam.org/item/AIF_2005__55_1_29_0/

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