Polygonal Billiards with One Sided Scattering
Annales de l'Institut Fourier, Volume 65 (2015) no. 5, pp. 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: 10.5802/aif.2975
Classification: 37C35, 03B10, 68R15
Keywords: Polygonal billiard, interval translation mapping, spy mirror, complexity
Mot clés : billard polygonal, translation d’intervalles, miroir espion, complexité
Skripchenko, Alexandra 1, 2; Troubetzkoy, Serge 3, 4

1 CNRS UMR 7586, Institut de Mathématiques de Jussieu - Paris Rive Gauche Batiment Sophie Germaine, Case 7021 75205 Paris Cedex 13 (France)
2 and Laboratory of Geometric Methods in Mathematical Physics, Lomonosov Moscow State University Moscow 119991 (Russia)
3 Aix Marseille Université, CNRS Centrale Marseille, I2M, UMR 7373 13453 Marseille (France)
4 Mailing address: I2M, Luminy, Case 907, 13288 Marseille CEDEX 9 (France)
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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/articles/10.5802/aif.2975/

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

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

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

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

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

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

[7] Cassaigne, J.; Hubert, P.; Troubetzkoy, S. Complexity and growth for polygonal billiards, Ann. Inst. Fourier (Grenoble), Volume 52 (2002) no. 3, pp. 835-847 | DOI | Numdam | MR | Zbl

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

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

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

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

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

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