English

Mixing for Smooth Time-Changes of General Nilflows

Dynamical Systems 2021-04-09 v2

Abstract

We consider completely irrational nilflows on any nilmanifold of step at least 22. 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 22) the main result proved in [AFU] for the special class of Heisenberg (step 22) 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.

Keywords

Cite

@article{arxiv.1905.11628,
  title  = {Mixing for Smooth Time-Changes of General Nilflows},
  author = {Artur Avila and Giovanni Forni and Davide Ravotti and Corinna Ulcigrai},
  journal= {arXiv preprint arXiv:1905.11628},
  year   = {2021}
}

Comments

44 pages, 1 figure. Several corrections and simplifications following the referee's suggestions. To appear in Advances in Mathematics

R2 v1 2026-06-23T09:28:17.205Z