Seminarios

When the injectivity radius of the surface is finite, it is known that horocycle trajectories are closed or have non minimal closure, except if the surface is "convex-cocompact". 

If we add the condition that the injectivity radius is >0, then all ergodic measure m, invariant by the horocycle flow are quasi-invariant ( i-e the image of m by any time of the geodesic flow is absolutely continuous with respect to m).

In this talk, I will explain how to construct a hyperbolic surface admitting a non trivial minimal set for the horocyclic flow and a conservative and ergodic invariant measure which is not quasi-invariant.