TY - JOUR

T1 - Mixing for time-changes of heisenberg nilflows

AU - Avila, Artur

AU - Forni, Giovanni

AU - Ulcigrai, Corinna

PY - 2011/11

Y1 - 2011/11

N2 - 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 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.

AB - 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 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.

UR - http://www.scopus.com/inward/record.url?scp=84862147781&partnerID=8YFLogxK

M3 - Article (Academic Journal)

AN - SCOPUS:84862147781

VL - 89

SP - 369

EP - 410

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

SN - 0022-040X

IS - 3

ER -