Dynamics Lunch: Jasmin Matz (Huji) ״Distribution of periodic orbits of the horocycle flow״

An old result of Hedlund tells us that there are no closed orbits for the horocycle flow on a compact Riemann surface M. The situation is different if M is non-compact in which case there is a one-parameter family of periodic orbits for every cusp of M. I want to talk about a result by Sarnak concerning the distribution of the such orbits in each of these families when their length goes to infinity. It turns out that these orbits become equidistributed in M and the rate of convergence can in fact be quantified in terms of spectral properties of the Eisenstein series on M.


Tue, 26/06/2018 - 12:00 to 13:00


Manchester lounge