Hausdorff dimension of non-uniquely ergodic directions in eigenform loci

Abstract

We consider the eigenform locus ${\mathcal{E}}_D$ in $\mathcal{H}(1,1)$ where $D$ is not a square. We prove that for any translation surface $(X,\omega )\in {\mathcal{E}}_D$, the set of non-uniquely ergodic directions has Hausdorff dimension $1/2$, except when $D=5$ and $(X,\omega )$ lies in the Teichmüller curve generated by the regular decagon.

28 pages