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arXiv · 1704.06303

On the Unique Ergodicity of Quadratic Differentials and the Orientation Double Cover

M. E. Smith
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Abstract

We construct an example of a uniquely ergodic measured foliation on a surface such that the associated translation flow on the orientation double cover is minimal but not uniquely ergodic. We then prove a geometric criterion for the horizontal foliation of a quadratic differential to be uniquely ergodic. The second theorem generalizes a result of Trevi\~no for the horizontal flow on a translation surface, as well as Masur's criterion for unique ergodicity of the horizontal foliation.

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M. E. Smith. 2017-04-20. On the Unique Ergodicity of Quadratic Differentials and the Orientation Double Cover. https://arxiv.org/abs/1704.06303

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