Time-changes of horocycle flows

Abstract

We consider smooth time-changes of the classical horocycle flows onthe unit tangent bundle of a compact hyperbolic surface and provesharp bounds on the rate of equidistribution and the rate ofmixing. We then derive results on the spectrum of smooth time-changesand show that the spectrum is absolutely continuous with respect tothe Lebesgue measure on the real line and that the maximal spectraltype is equivalent to Lebesgue.