Nicolas Bedaride, Pascal Hubert
Published 2011-09-29Version 1
We consider the billiard map in the hypercube of $\mathbb{R}^d$. 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.
Comments: 18 pages, 3 figures
Journal: Annales de l'institut Fourier. 2007, 57 (3) 719-738
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On the complexity of subshifts and infinite words
On the complexity function for sequences which are not uniformly recurrent
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