Abstract
We consider reparametrizations of Heisenberg nilflows. We show that if a Heisenberg nilflow is uniquely ergodic, all non-trivial time-changes 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. Mixing is produced by a mechanism known as stretching of Birkhoff sums. The complement of the set of mixing time-changes (or, equivalently, of mixing roof functions) has countable codimension and can be explicitely described in terms of the invariant distributions for the nilflow (or, equivalently, for the skew-shift), allowing to produce concrete examples of mixing time-changes.
Translated title of the contribution | Mixing for Time-Changes of Heisenberg Nilflows |
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Original language | English |
Pages (from-to) | 369-410 |
Number of pages | 42 |
Journal | Journal of Differential Geometry |
Volume | 89 |
Issue number | 3 |
Publication status | Published - 2011 |