Journal of Modern Dynamics (JMD)

Time-changes of horocycle flows

Pages: 251 - 273, Issue 2, April 2012      doi:10.3934/jmd.2012.6.251

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Giovanni Forni - Department of Mathematics, University of Maryland, College Park, MD 20742-4015, United States (email)
Corinna Ulcigrai - School of Mathematics, University of Bristol, University Walk, Clifton, BS8 1TW,Bristol, United Kingdom (email)

Abstract: 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.

Keywords:  Time-changes, horocycle flows, quantitative equidistribution, quantitative mixing, spectral theory.
Mathematics Subject Classification:  Primary: 37A25, 37A30, 37C10, 37C40, 37D40.

Received: February 2012;      Available Online: August 2012.