Singularity of projections of 2-dimensional measures invariant under the geodesic flow

Details Singularity of projections of 2-dimensional measures invariant under the geodesic flow Singularity of projections of 2-dimensional measures invariant under the geodesic flow

2011-04-14

arxiv.org/abs/1104.2687v1

Mathematics

Dynamical Systems

12 pages

Scientific paper

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.

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