# Dynamics of $\mathrm{SL}_2(\mathbb{R})$ over moduli space in genus two

### Abstract

This paper classifies orbit closures and invariant measures for the natural action of $\operatorname{SL}_2(\mathbb{R})$ on $\Omega \mathcal{M}_2$, the bundle of holomorphic 1-forms over the moduli space of Riemann surfaces of genus two.

## Authors

Curtis T. McMullen

Department of Mathematics, Harvard University, Cambridge, MA 02138, United States