Texas A&M University, Department of
Mathematics, 216 Milner Hall, 19th of October 2005, 3:00-3:50
Groups and Dynamics Seminar
Invariant measures
for the horocycle flow on periodic surfaces
François Ledrappier of
University of Notre Dame
The horocycle flow of a geometrically infinite hyperbolic surface may
preserve more than one non-trivial ergodic invariant Radon measure. In
a joint work with Omri Sarig, we classify these measures in case the
surface is a regular cover of a compact hyperbolic surface, by
constructing a bijection between them and the positive minimal
eigenfunctions of the associated Laplace-Beltrami operator. In this
talk, we'll give some background and some examples.