Giovanni Forni

University of Maryland

On Mixing rates for time-changes of Heisenberg Nilflows

Ergodic Theory and Dynamical Systems Seminar

8th January 2018, 1:30 pm – 2:30 pm
Howard House, 4th Floor Seminar Room

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. The main applications are polynomial mixing rates for non-trivial time-changes
(improving on a result by Avila, Ulcigrai and myself that such flows are mixing), and
limit theorems for Heisenberg nilflows (extending in part results of Griffin and Marklof and
Cellarosi and Marklof on the related question of limit distributions of theta sum).

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