Billiard complexity in the hypercube
  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. 
Nicolas Bedaride and Pascal Hubert
math.DS math.CO