Abstract
A stable periodic billiard path in a triangle is a billiard path which persists under small perturbations of the triangle. This article gives a geometric proof that no right triangles have stable periodic billiard paths.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Galperin G., Zvonkine D. (2003) Periodic billiard trajectories in right triangles and right-angled tetrahedra. Regul. Chaotic Dyn. 8(1): 29–44 MR 1963966 (2004b:37081)
Tabachnikov, S.: Billiards. Panor. Synth. (1), vi+142 (1995) MR 1328336 (96c:58134)
Thurston, W. P.: Three-dimensional geometry and topology, vol. 1. In: Levy, S. (ed.) Princeton Mathematical Series, vol.~35, Princeton University Press, Princeton, NJ (1997) MR 1435975 (97m:57016)
Troubetzkoy, S.: Periodic billiard orbits in right triangles, Ann. Inst. Fourier (Grenoble) 55(1), 29–46 (2005). http://arxiv.org/abs/math/0405280 MR 2141287
Troubetzkoy, S.: Periodic billiard orbits in right triangles II. arXiv:math.DS/0505637 (2005). http://arxiv.org/abs/math/0405280
Vorobets Ya.B., Galperin G.A., Stëpin A.M. (1991) Periodic billiard trajectories in polygons. Usp. Mat. Nauk 46(5(281)), 165–166 MR 1160340 (93b:58119)
Zemljakov A.N., Katok A.B. (1975) Topological transitivity of billiards in polygons. Mat. Zametki 18(2): 291–300 MR 0399423 (53 #3267)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hooper, W.P. Periodic billiard paths in right triangles are unstable. Geom Dedicata 125, 39–46 (2007). https://doi.org/10.1007/s10711-007-9129-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10711-007-9129-9