no. 3
Billiard complexity in the hypercube
[Complexité du billard cubique multi-dimensionnel]
Bedaride, Nicolas1 ; Hubert, Pascal2
1 Fédération de recherches des unités de mathématiques de Marseille UMR 6632 Laboratoire d’Analyse Topologie et Probabilités Av. Escadrille Normandie-Niemen 13397 Marseille Cedex 20 (France)
2 Fédération de recherches des unités de mathématiques de Marseille UMR 6632 Laboratoire d’Analyse Topologie et Probabilités av. Escadrille Normandie-Niemen 13397 Marseille Cedex 20 (France)
Annales de l'Institut Fourier, Tome 57 (2007) no. 3, pp. 719-738.

On considère l’application du billard dans le cube de ℝ d . On code cette application par les faces du cube. On obtient un langage, dont on cherche à évaluer la complexité. On montre que l’ordre de grandeur de cette fonction est n 3d-3 .

We consider the billiard map in the hypercube of ℝ d . We obtain a language by coding the billiard map by the faces of the hypercube. We investigate the complexity function of this language. We prove that n 3d-3 is the order of magnitude of the complexity.

DOI : 10.5802/aif.2274
Classification : 37A35, 37C35, 05A16, 11N37, 28D
Keywords: Symbolic dynamic, billiard, words, complexity function
Mot clés : Dynamique symbolique, billard, mots, complexité
Bedaride, Nicolas 1 ; Hubert, Pascal 2

1 Fédération de recherches des unités de mathématiques de Marseille UMR 6632 Laboratoire d’Analyse Topologie et Probabilités Av. Escadrille Normandie-Niemen 13397 Marseille Cedex 20 (France)
2 Fédération de recherches des unités de mathématiques de Marseille UMR 6632 Laboratoire d’Analyse Topologie et Probabilités av. Escadrille Normandie-Niemen 13397 Marseille Cedex 20 (France) 
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Bedaride, Nicolas; Hubert, Pascal. Billiard complexity in the hypercube. Annales de l'Institut Fourier, Tome 57 (2007) no. 3, pp. 719-738. doi : 10.5802/aif.2274. http://archive.numdam.org/articles/10.5802/aif.2274/

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