Multiple mixing and disjointness for time changes of bounded-type Heisenberg nilflows
Journal de l’École polytechnique — Mathématiques, Volume 7 (2020), pp. 63-91.

We study time changes of bounded type Heisenberg nilflows (ϕ t ) acting on the Heisenberg nilmanifold M. We show that for every positive τW s (M), s>7/2, every non-trivial time change (ϕ t τ ) enjoys the Ratner property. As a consequence, every mixing time change is mixing of all orders. Moreover, we show that for every τW s (M), s>9/2 and every p,q, pq, (ϕ pt τ ) and (ϕ qt τ ) are disjoint. As a consequence, Sarnak conjecture on Möbius disjointness holds for all such time changes.

Nous étudions les reparamétrisations (ϕ t τ ) des flots nilpotents de Heisenberg de type borné sur une variété nilpotente de Heisenberg M. Nous montrons que, pour des fonctions positives τW s (M) (espace de Sobolev) avec s>7/2, toute reparamétrisation non triviale (ϕ t τ ) a la propriété de Ratner. En conséquence, toute reparamétrisation mélangeante est mélangeante de tous les ordres. De plus, nous montrons que pour toutes les fonctions τW s (M), avec s>9/2 et pour tous p,q, pq, les flots (ϕ pt τ ) et (ϕ qt τ ) sont disjoints. Il s’ensuit, en particulier, que la conjecture de Sarnak sur la disjonction de la fonction de Möbius est valable pour toutes ces reparamétrisations.

Received:
Accepted:
Published online:
DOI: 10.5802/jep.111
Classification: 37C40,  28D10
Keywords: Nilflows, time-changes, Ratner property, multiple mixing, disjointness
Giovanni Forni 1; Adam Kanigowski 1

1 Department of Mathematics, University of Maryland 4176 Campus Drive – William E. Kirwan Hall, College Park, MD 20742-4015, USA
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Giovanni Forni; Adam Kanigowski. Multiple mixing and disjointness for time changes of bounded-type Heisenberg nilflows. Journal de l’École polytechnique — Mathématiques, Volume 7 (2020), pp. 63-91. doi : 10.5802/jep.111. https://jep.centre-mersenne.org/articles/10.5802/jep.111/

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