%0 Journal Article
%T Classification of rotations on the torus $\mathbb{T}^2$
%+ Laboratoire d'Analyse, Topologie, Probabilités (LATP)
%A Bedaride, Nicolas
%Z 18 pages, 4 figures
%< avec comité de lecture
%Z LATP:12-050
%@ 1879-2294
%J Theoretical Computer Science
%I Elsevier
%V 385
%N 1-3
%P 214-225
%8 2007
%D 2007
%Z 1205.5093
%R 10.1016/j.tcs.2007.05.037
%K Billiard
%K Symbolic dynamic
%K Words
%K Complexity
%K Sturmian words
%Z Mathematics [math]/Dynamical Systems [math.DS]
%Z Mathematics [math]/Combinatorics [math.CO]Journal articles
%X 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.
%G English
%L hal-00920743
%U https://hal.science/hal-00920743
%~ LATP
%~ CNRS
%~ UNIV-AMU
%~ I2M
%~ TDS-MACS