  We consider smooth time-changes of the classical horocycle flows on the unit
tangent bundle of a compact hyperbolic surface and prove sharp bounds on the
rate of equidistribution and the rate of mixing. We then derive results on the
spectrum of smooth time-changes and show that the spectrum is absolutely
continuous with respect to the Lebesgue measure on the real line and that the
maximal spectral type is equivalent to Lebesgue.

Dynamical Systems