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 . 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 ) the main result proved in [AFU] for the special class of Heisenberg (step ) 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