Unique Ergodicity For Infinite Area Translation Surfaces

2019/08/12 by Sabogal, Alba Málaga, Troubetzkoy, Serge
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1908.04019

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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