Mixing for the time-changes of Heisenberg nilflows. (English) Zbl 1281.37012

Avila, Artur; Forni, Giovanni; Ulcigrai, Corinna

J. Differ. Geom. 89, No. 3, 369-410 (2011).

This paper is a contribution to the smooth ergodic theory of parabolic flows. In Section 2, the definitions of Heisenberg nilflows, special flows and time-changes are given. Theorem 3 contains the main results for time-changes of nilflows.
In Section 3, the authors prove that non-triviality of the time-change guarantees that there is a stretch of ergodic sums. Using this stretch, they prove the mixing in Section 4.
Section 5 contains the proof of the effective characterization of non-trivial time-changes, which allows to exhibit explicit examples of mixing time-changes.

Reviewer: Victor Sharapov (Volgograd)

MSC:

37C40	Smooth ergodic theory, invariant measures for smooth dynamical systems
37A25	Ergodicity, mixing, rates of mixing

Keywords:

mixing; ergodic; nilflow; flow