Density of mild mixing property for vertical flows of Abelian differentials

Abstract

We prove that if $g\ge 2$ then the set of all Abelian differentials $(M,\omega )$ for which the vertical flow is mildly mixing is dense in every stratum of the moduli space ${\mathcal{H}}_g$. The proof is based on a sufficient condition for special flows over irrational rotations and under piecewise constant roof functions to be mildly mixing.

14 pages