Singularity of projections of 2-dimensional measures invariant under the geodesic flow
arXiv:1104.2687 · doi:10.1007/s00220-011-1387-6
Abstract
We show that on any compact Riemann surface with variable negative curvature there exists a measure which is invariant and ergodic under the geodesic flow and whose projection to the base manifold is 2-dimensional and singular with respect to the 2-dimensional Lebesgue measure.
12 pages