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

F. Ledrappier (1) , R. Hovila , E. Järvenpää , M. Järvenpää

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Domaines: Probabilités [math.PR]

F. Ledrappier, R. Hovila, E. Järvenpää, M. Järvenpää. Singularity of projections of 2-dimensional measures invariant under the geodesic flow. Communications in Mathematical Physics, 2012, 312, pp.127-136. ⟨10.1007/s00220-011-1387-6⟩. ⟨hal-00705225⟩