Singularity of projections of 2-dimensional measures invariant under the geodesic flow
Dynamical Systems
2015-05-27 v1 Mathematical Physics
Differential Geometry
math.MP
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.
Cite
@article{arxiv.1104.2687,
title = {Singularity of projections of 2-dimensional measures invariant under the geodesic flow},
author = {Risto Hovila and Esa Järvenpää and Maarit Järvenpää and François Ledrappier},
journal= {arXiv preprint arXiv:1104.2687},
year = {2015}
}
Comments
12 pages