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arXiv · 1205.5093

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

Nicolas Bédaride
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Abstract

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.

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Nicolas Bédaride. 2012-05-23. Classification of rotations on the torus $\mathbb{T}^2$. https://arxiv.org/abs/1205.5093

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