We consider the billiard map in the hypercube of . 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 is the order of magnitude of the complexity.
On considère l’application du billard dans le cube de . 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 .
Keywords: Symbolic dynamic, billiard, words, complexity function
Mot clés : Dynamique symbolique, billard, mots, complexité
@article{AIF_2007__57_3_719_0, author = {Bedaride, Nicolas and Hubert, Pascal}, title = {Billiard complexity in the hypercube}, journal = {Annales de l'Institut Fourier}, pages = {719--738}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {57}, number = {3}, year = {2007}, doi = {10.5802/aif.2274}, zbl = {1138.37017}, mrnumber = {2336827}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2274/} }
TY - JOUR AU - Bedaride, Nicolas AU - Hubert, Pascal TI - Billiard complexity in the hypercube JO - Annales de l'Institut Fourier PY - 2007 SP - 719 EP - 738 VL - 57 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2274/ DO - 10.5802/aif.2274 LA - en ID - AIF_2007__57_3_719_0 ER -
%0 Journal Article %A Bedaride, Nicolas %A Hubert, Pascal %T Billiard complexity in the hypercube %J Annales de l'Institut Fourier %D 2007 %P 719-738 %V 57 %N 3 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2274/ %R 10.5802/aif.2274 %G en %F AIF_2007__57_3_719_0
Bedaride, Nicolas; Hubert, Pascal. Billiard complexity in the hypercube. Annales de l'Institut Fourier, Volume 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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