Weak mixing for interval exchange transformations and translation flows


We prove 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 typical translation surface of genus $g \geq 2$ (with prescribed singularity types) is weakly mixing.


Artur Ávila

CNRS UMR 7599, Université Pierre et Marie Curie, 75252 Paris, France

Giovanni Forni

Department of Mathematics, University of Toronto, Toronto, ON, Canada M5S 2E4