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Pré-Publication, Document De Travail Année : 2019

Unique ergodicity for infinite area Translation Surfaces

Résumé

We consider infinite staircase translation surfaces with varying step sizes. For typical step sizes we show that the translation flow is uniquely ergodic in almost every direction. Our result also hold for typical configurations of the Ehrenfest wind-tree model endowed with the Hausdorff topology. In contrast, we show that the translation flow on a periodic translation surface can not be uniquely ergodic in any direction.
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Dates et versions

hal-02265283 , version 1 (09-08-2019)
hal-02265283 , version 2 (21-07-2023)

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Citer

Alba Málaga Sabogal, Serge Troubetzkoy. Unique ergodicity for infinite area Translation Surfaces. 2019. ⟨hal-02265283v1⟩
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