2008-02-22

John Hubbard, Cornell University

The equidistribution of horocycles on hyperbolic surfaces

I propose to give a proof that every horocycle on a hyperbolic surface of finite area is either periodic or equidistributed. This result is often attributed to Ratner, but really due to Smillie and Dani. The proof I will present is not really significantly different from theirs, but at certain points it is more geometric.