Polygonal Billiards with One Sided Scattering  [ Billards polygonaux avec dispersion unilatérale ]
Annales de l'Institut Fourier, Tome 65 (2015) no. 5, p. 1881-1896
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.
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.
DOI : https://doi.org/10.5802/aif.2975
Classification:  37C35,  03B10,  68R15
Mots clés: billard polygonal, translation d’intervalles, miroir espion, complexité 
@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, Tome 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