MINIMALITY AND UNIQUE ERGODICITY OF VEECH 1969 TYPE INTERVAL EXCHANGE TRANSFORMATIONS

Sébastien Ferenczi (1) , Pascal Hubert

1 I2M - Institut de Mathématiques de Marseille

We give conditions for minimality of Z/N Z extensions of a rotation of angle α 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 Z/N 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.

Domaines: Mathématiques [math]

Sébastien Ferenczi, Pascal Hubert. MINIMALITY AND UNIQUE ERGODICITY OF VEECH 1969 TYPE INTERVAL EXCHANGE TRANSFORMATIONS. 2021. ⟨hal-03446722⟩