Open Access
November 2011 Mixing for the time-changes of Heisenberg nilflows
Artur Avila, Giovanni Forni, Corinna Ulcigrai
J. Differential Geom. 89(3): 369-410 (November 2011). DOI: 10.4310/jdg/1335207373


We consider reparametrizations of Heisenberg nilflows.We show that if a Heisenberg nilflow is uniquely ergodic, all non-trivial timechanges within a dense subspace of smooth time-changes are mixing. Equivalently, in the language of special flows, we consider special flows over linear skew-shift extensions of irrational rotations of the circle. Without assuming any Diophantine condition on the frequency, we define a dense class of smooth roof functions for which the corresponding special flows are mixing whenever the roof function is not a coboundary. Mixing is produced by a mechanism known as stretching of ergodic sums. The complement of the set of mixing time-changes (or, equivalently, of mixing roof functions) has countable codimension and can be explicitly described in terms of the invariant distributions for the nilflow (or, equivalently, for the skew-shift), producing concrete examples of mixing time-changes.


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Artur Avila. Giovanni Forni. Corinna Ulcigrai. "Mixing for the time-changes of Heisenberg nilflows." J. Differential Geom. 89 (3) 369 - 410, November 2011.


Published: November 2011
First available in Project Euclid: 23 April 2012

zbMATH: 1281.37012
MathSciNet: MR2879246
Digital Object Identifier: 10.4310/jdg/1335207373

Rights: Copyright © 2011 Lehigh University

Vol.89 • No. 3 • November 2011
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