Billiard complexity in the hypercube

Published 29 Sep 2011 in math.DS and math.CO | (1109.6410v1)

Abstract: 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.

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