JMD
Weak mixing for logarithmic flows over interval exchange transformations
Corinna Ulcigrai
We consider a class of special flows over interval exchange transformations which includes roof functions with symmetric logarithmic singularities. We prove that such flows are typically weakly mixing. As a corollary, minimal flows given by multivalued Hamiltonians on higher-genus surfaces are typically weakly mixing.
keywords: logarithmic singularities area-preserving flows on surfaces. Weak mixing interval exchange transformations
JMD
Time-changes of horocycle flows
Giovanni Forni Corinna Ulcigrai
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 mixing spectral theory. quantitative equidistribution

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