Corinna Ulcigrai (Bristol)
On the spectrum of time-changes of horocycle flows
Abstract: The horocycle flow on a compact hyperbolic surface is a classical dynamical flow whose ergodic and spectral properties have been studied in great detail. If one considers the simplest possible perturbations -time changes- though, it turns out that very little is known for generic smooth time-changes of the horocycle flow. After reviewing some properties of the classical horocycle flow, in this talk we will focus on the nature of the spectrum and the mixing properties of its time-changes. In particular, in joint work with G. Forni (Maryland) we proved a conjecture by Katok and Thouvenot, by showing that the spectrum of all smooth time-changes of horocycle flows is absolutely continuous (and in fact, Lebesgue).