The Cohomological Equation and Invariant Distributions for Horocycle Maps

Abstract

We study the invariant distributions for the horocycle map on $\Gamma \backslash SL(2,\mathbb{R})$ and prove Sobolev estimates for the cohomological equation of the horocycle map. As an application, we obtain an estimate for the rate of equidistribution for horocycle maps on compact manifolds.

arXiv comment44 pages