Billiard complexity in the hypercube
Annales de l'Institut Fourier, Volume 57 (2007) no. 3, p. 719-738
We consider the billiard map in the hypercube of 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.
On considère l’application du billard dans le cube de 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 .
DOI : https://doi.org/10.5802/aif.2274
Classification:  37A35,  37C35,  05A16,  11N37,  28D
Keywords: Symbolic dynamic, billiard, words, complexity function
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {57},
     number = {3},
     year = {2007},
     pages = {719-738},
     doi = {10.5802/aif.2274},
     zbl = {1138.37017},
     mrnumber = {2336827},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2007__57_3_719_0}
}
Billiard complexity in the hypercube. Annales de l'Institut Fourier, Volume 57 (2007) no. 3, pp. 719-738. doi : 10.5802/aif.2274. https://aif.centre-mersenne.org/item/AIF_2007__57_3_719_0/

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