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JMD

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.

JMD

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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