Billiard complexity in the hypercube

Details Billiard complexity in the hypercube Billiard complexity in the hypercube

2011-09-29

arxiv.org/abs/1109.6410v1

Annales de l'institut Fourier. 2007, 57 (3) 719-738

Mathematics

Dynamical Systems

18 pages, 3 figures

Scientific paper

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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