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arXiv · 1404.4657

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

Jayadev S. Athreya·Jon Chaika
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Abstract

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

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Jayadev S. Athreya, Jon Chaika. 2014-09-14. The Hausdorff Dimension of Non-Uniquely Ergodic directions in $\mathcal{H}(2)$ is almost everywhere $1/2$. https://doi.org/10.2140/gt.2015.19.3537

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