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

By Risto Hovila, Esa Järvenpää, Maarit Järvenpää and François Ledrappier

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.Comment: 12 page

Topics: Mathematics - Dynamical Systems, Mathematical Physics, Mathematics - Differential Geometry, 37C45, 53D25, 37D20, 28A80
Year: 2011
DOI identifier: 10.1007/s00220-011-1387-6
OAI identifier: oai:arXiv.org:1104.2687
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