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arXiv · 1905.11628

Mixing for Smooth Time-Changes of General Nilflows

Artur Avila·Giovanni Forni·Davide Ravotti·Corinna Ulcigrai
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Abstract

We consider completely irrational nilflows on any nilmanifold of step at least $2$. We show that there exists a dense set of smooth time-changes such that any time-change in this class which is not measurably trivial gives rise to a mixing nilflow. This in particular reproves and generalizes to any nilflow (of step at least $2$) the main result proved in [AFU] for the special class of Heisenberg (step $2$) nilflows, and later generalized in [Rav2] to a class of nilflows of arbitrary step which are isomorphic to suspensions of higher-dimensional linear toral skew-shifts.

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Artur Avila, Giovanni Forni, Davide Ravotti, Corinna Ulcigrai. 2019-05-28. Mixing for Smooth Time-Changes of General Nilflows. https://arxiv.org/abs/1905.11628

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