Polygonal Billiards with One Sided Scattering
Annales de l'Institut Fourier, Volume 65 (2015) no. 5, p. 1881-1896

We study the billiard on a square billiard table with a one-sided vertical mirror. We associate trajectories of these billiards with double rotations and study orbit behavior and questions of complexity.

Nous étudions le billard sur une table carrée avec un miroir vertical à une face. Nous associons les trajectoires de ces billards à des doubles rotations et étudions le comportement des orbites et des questions de complexité.

DOI : https://doi.org/10.5802/aif.2975
Classification:  37C35,  03B10,  68R15
Keywords: Polygonal billiard, interval translation mapping, spy mirror, complexity
@article{AIF_2015__65_5_1881_0,
     author = {Skripchenko, Alexandra and Troubetzkoy, Serge},
     title = {Polygonal Billiards with One Sided Scattering},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {65},
     number = {5},
     year = {2015},
     pages = {1881-1896},
     doi = {10.5802/aif.2975},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2015__65_5_1881_0}
}
Skripchenko, Alexandra; Troubetzkoy, Serge. Polygonal Billiards with One Sided Scattering. Annales de l'Institut Fourier, Volume 65 (2015) no. 5, pp. 1881-1896. doi : 10.5802/aif.2975. http://www.numdam.org/item/AIF_2015__65_5_1881_0/

[1] Baillif, Mathieu A polynomial bound for the lap number, Qual. Theory Dyn. Syst., Tome 3 (2002) no. 2, pp. 325-329 | Article | Zbl 1057.37035

[2] Boshernitzan, Michael; Kornfeld, Isaac Interval translation mappings, Ergodic Theory Dynam. Systems, Tome 15 (1995) no. 5, pp. 821-832 | Article | Zbl 0836.58026

[3] Bruin, H. Renormalization in a class of interval translation maps of d branches, Dyn. Syst., Tome 22 (2007) no. 1, pp. 11-24 | Article | Zbl 1115.37038

[4] Bruin, H.; Troubetzkoy, S. The Gauss map on a class of interval translation mappings, Israel J. Math., Tome 137 (2003), pp. 125-148 | Article | Zbl 1274.37005

[5] Bruin, Henk; Clack, Gregory Inducing and unique ergodicity of double rotations, Discrete Contin. Dyn. Syst., Tome 32 (2012) no. 12, pp. 4133-4147 | Article | Zbl 1263.37020

[6] Buzzi, Jérôme; Hubert, Pascal Piecewise monotone maps without periodic points: rigidity, measures and complexity, Ergodic Theory Dynam. Systems, Tome 24 (2004) no. 2, pp. 383-405 | Article | Zbl 1076.37022

[7] Cassaigne, J.; Hubert, P.; Troubetzkoy, S. Complexity and growth for polygonal billiards, Ann. Inst. Fourier (Grenoble), Tome 52 (2002) no. 3, pp. 835-847 http://aif.cedram.org/item?id=AIF_2002__52_3_835_0 | Zbl 1115.37312

[8] Cassaigne, Julien Complexité et facteurs spéciaux, Bull. Belg. Math. Soc. Simon Stevin, Tome 4 (1997) no. 1, pp. 67-88 http://projecteuclid.org/euclid.bbms/1105730624 (Journées Montoises (Mons, 1994)) | Zbl 0921.68065

[9] Ferenczi, Sébastien; Monteil, Thierry Infinite words with uniform frequencies, and invariant measures, Combinatorics, automata and number theory, Cambridge Univ. Press, Cambridge (Encyclopedia Math. Appl.) Tome 135 (2010), pp. 373-409 | Zbl 1217.68168

[10] Masur, Howard; Tabachnikov, Serge Rational billiards and flat structures, Handbook of dynamical systems, Vol. 1A, North-Holland, Amsterdam (2002), pp. 1015-1089 | Article | Zbl 1057.37034

[11] Schmeling, J.; Troubetzkoy, S. Interval translation mappings, Dynamical systems (Luminy-Marseille, 1998), World Sci. Publ., River Edge, NJ (2000), pp. 291-302 | Zbl 1196.37072

[12] Suzuki, Hideyuki; Ito, Shunji; Aihara, Kazuyuki Double rotations, Discrete Contin. Dyn. Syst., Tome 13 (2005) no. 2, pp. 515-532 | Article | Zbl 1078.37033