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

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.

MSC:

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

Keywords:

mixing; ergodic; nilflow; flow
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