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arXiv · 2103.09018

Minimality and unique ergodicity of Veech 1969 type interval exchange transformations

Sébastien Ferenczi·Pascal Hubert
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Abstract

We give conditions for minimality of $\mathbb Z/N\mathbb Z$ extensions of a rotation of angle $\alpha$ with one marked point, solving the problem for any prime $N$: for $N=2$, these correspond to the Veech 1969 examples, for which a necessary and sufficient condition was not known yet. We provide also a word combinatorial criterion of minimality valid for general interval exchange transformations, which applies to $\mathbb Z/N\mathbb Z$ extensions of any interval exchange transformation with any number of marked points. Then we give a condition for unique ergodicity of these extensions when the initial interval exchange transformation is linearly recurrent and there are one or two marked points.

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Sébastien Ferenczi, Pascal Hubert. 2021-03-16. Minimality and unique ergodicity of Veech 1969 type interval exchange transformations. https://arxiv.org/abs/2103.09018

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