Omri Sarig (PSU)

will speak

Invariant measures for the horocycle flow on periodic hyperbolic surfaces

(joint with F. Ledrappier)

Abstract:

The horocycle flow of a hyperbolic surface of finite volume has just one non-trivial ergodic invariant Radon measure up to a constant (Furstenberg, Dani, Smillie). I will describe the situation for a class of infinite volume surfaces: periodic surfaces. It turns out that in this case the collection of ergodic invariant Radon measures is richer, although it can still be described. This description is in terms of the positive eigenfunctions of the Laplacian of the surface. If the surface has polynomial growth, the ergodic invariant Radon measures can be completely enumerated.

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Last update on 20/10/02.