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Singularity of Projections of 2-Dimensional Measures Invariant Under the Geodesic Flow |
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| Authors: | Risto Hovila Esa J?rvenp?? Maarit J?rvenp?? Fran?ois Ledrappier |
| Affiliation: | 1. Department of Mathematics and Statistics, University of Helsinki, P. O. Box 68, 00014, Helsinki, Finland 2. Department of Mathematical Sciences, University of Oulu, P. O. Box 3000, 90014, Oulu, Finland 3. LPMA, UMR 7599, Universit?? Paris 6, 4, Place Jussieu, 75252, Paris Cedex 05, France |
| 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. |
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