For some classes of hyperbolic surfaces, all locally finite ergodic measures invariant under the horocycle flow are described. See the works of Omri Sarig and those of Lindenstrauss-Landesberg in that sense. This talk focuses on the study of another class of hyperbolic surfaces. Precisely, we give an analytical construction of a family of surfaces of infinite type whose corresponding horocycle flow is conservative but not ergodic with respect to the Liouville measure.
DR. Cheikh lo
University of Cheikh Anta Diop of Dakar
Geometry and Topology