Time-changes of horocycle flows

Giovanni Forni, Corinna Ulcigrai

Research output: Contribution to journalArticle (Academic Journal)peer-review

26 Citations (Scopus)


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.
Original languageEnglish
Article number5
Pages (from-to)251-273
Number of pages23
JournalJournal of Modern Dynamics
Issue number2
Publication statusPublished - Apr 2012


  • Time-changes, horocycle flows, quantitative equidistribution, quantitative mixing, spectral theory


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