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Weak mixing for interval exchange transformations and translation flows

Artur Avila·Giovanni Forni
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Abstract

We show that a typical interval exchange transformation is either weakly mixing or it is an irrational rotation. We also conclude that a typical translation flow on a surface of genus $g \geq 2$ (with prescribed singularity types) is weakly mixing.

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Artur Avila, Giovanni Forni. 2004-06-16. Weak mixing for interval exchange transformations and translation flows. https://arxiv.org/abs/math/0406326

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