Classification of rotations on the torus $\mathbb{T}^2$

Nicolas Bedaride (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We consider rotations on the torus $\mathbb{T}^2$, and we classify them with respect to the complexity functions. In dimension one, a minimal rotation can be coded by a sturmian word. A sturmian word has complexity $n+1$ by the Morse-Hedlund theorem. Here we make a generalization in dimension two.

Mots clés: Billiard; Symbolic dynamic; Words; Complexity; Sturmian words

Domaines: Systèmes dynamiques [math.DS]; Combinatoire [math.CO]

Nicolas Bedaride. Classification of rotations on the torus $\mathbb{T}^2$. Theoretical Computer Science, 2007, 385 (1-3), pp.214-225. ⟨10.1016/j.tcs.2007.05.037⟩. ⟨hal-00920743⟩