Mutliple mixing and disjointness for time changes of bounded-type Heisenberg nilflows

Abstract

We study time changes of bounded type Heisenberg nilflows $({\varphi }_t)$ acting on the Heisenberg nilmanifold $M$. We show that for every positive $\tau \in W^s(M)$, $s>7/2$, every non-trivial time change $({\varphi }_t^{\tau })$ enjoys the Ratner property. As a consequence every mixing time change is mixing of all orders. Moreover we show that for every $\tau \in W^s(M)$, $s>9/2$ and every $p,q\in \mathbb{N}$, $p\ne q$, $({\varphi }_{pt}^{\tau })$ and $({\varphi }_{qt}^{\tau })$ are disjoint. As a consequence Sarnak's Conjecture on Möbius disjointness holds for all such time changes.

Cited by in corpus (3)

• Rigidity of joinings for some measure preserving systems
• Effective equidistribution for generalized higher step nilflows
• On the ergodic properties of time changes of partially hyperbolic homogeneous flows