Time-Changes of Horocycle Flows

Details Time-Changes of Horocycle Flows Time-Changes of Horocycle Flows

2012-02-22

arxiv.org/abs/1202.4986v2

Mathematics

Dynamical Systems

20 pages

Scientific paper

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.

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