The Hausdorff Dimension of Non-Uniquely Ergodic directions in $\mathcal{H}(2)$ is almost everywhere $1/2$

Abstract

We show that for almost every (with respect to Masur-Veech measure) $\omega \in \mathcal{H}(2)$, the set of angles $\theta \in [0,2\pi )$ so that $e^{i\theta }\omega$ has non-uniquely ergodic vertical foliation has Hausdorff dimension (and codimension) $1/2$.

Comprehensive rewrite. Hausdorff dimension lower bound axiomatized

Cited by in corpus (2)

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