Billiard complexity in the hypercube

Nicolas Bedaride; Pascal Hubert

Billiard complexity in the hypercube

Dynamical Systems 2011-09-30 v1 Combinatorics

Authors: Nicolas Bedaride , Pascal Hubert

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.

Keywords

billiards

Cite

@article{arxiv.1109.6410,
  title  = {Billiard complexity in the hypercube},
  author = {Nicolas Bedaride and Pascal Hubert},
  journal= {arXiv preprint arXiv:1109.6410},
  year   = {2011}
}

Comments

18 pages, 3 figures

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