On mixing rates for time-changes of Heisenberg nilflows

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Giovanni Forni
University of Maryland

We construct Bufetov functionals for nilpotent flows on (compact) Heisenberg nilmanifolds. Such functionals were first constructed by Bufetov for Interval Exchange Transformations and Translation flows, and later for horocycle flows by Bufetov and myself with the goal of proving limit theorems. In the Heisenberg case we generalize results of Griffin and Marklof, and Cellarosi and Marklof on the related question of limit distributions of theta sum. We then prove that in the Heisenberg case the functionals are real analytic along the leaves of a 2-dimensional foliation transverse to the flow and derive polynomial or ``stretched'' polynomial mixing rates for non-trivial time-changes (improving on a result by Avila, Ulcigrai and myself that such flows are mixing).