Weak mixing for interval exchange transformations and translation flows

Abstract

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.

Authors

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