The cohomological equation and invariant distributions for horocycle maps

JAMES TANIS
2012 Ergodic Theory and Dynamical Systems  
We study the invariant distributions for the horocycle map on Γ SL(2, 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.
doi:10.1017/etds.2012.125 fatcat:nlfrequq5be2xdgcbbz3sj4qcy