Polygonal Billiards with One Sided Scattering
[Billards polygonaux avec dispersion unilatérale]
Skripchenko, Alexandra1, 2 ; Troubetzkoy, Serge3, 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)
Annales de l'Institut Fourier, Tome 65 (2015) no. 5, pp. 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 : 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, Tome 65 (2015) no. 5, pp. 1881-1896. doi : 10.5802/aif.2975. http://www.numdam.org/articles/10.5802/aif.2975/

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