UNIQUE ERGODICITY FOR INFINITE AREA TRANSLATION SURFACES

Abstract : 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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Submitted on : Friday, August 9, 2019 - 10:56:40 AM
Last modification on : Tuesday, August 13, 2019 - 1:15:47 AM

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  • HAL Id : hal-02265283, version 1
  • ARXIV : 1908.04019

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Alba Málaga Sabogal, Serge Troubetzkoy. UNIQUE ERGODICITY FOR INFINITE AREA TRANSLATION SURFACES. 2019. ⟨hal-02265283⟩

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