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.
Classification: 37C27, 37E05, 37B99
Keywords: Polygonal billiard, periodic orbits, symmetries
@article{AIF_2005__55_1_29_0,
author = {Troubetzkoy, Serge},
title = {Periodic billiard orbits in right triangles},
journal = {Annales de l'Institut Fourier},
publisher = {Association des Annales de l'institut Fourier},
volume = {55},
number = {1},
year = {2005},
pages = {29-46},
doi = {10.5802/aif.2088},
zbl = {1063.37022},
mrnumber = {2141287},
language = {en},
url = {http://www.numdam.org/item/AIF_2005__55_1_29_0}
}
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. http://www.numdam.org/item/AIF_2005__55_1_29_0/
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