Multiple mixing and disjointness for time changes of bounded-type Heisenberg nilflows
Giovanni Forni; Adam Kanigowski
Journal de l'École polytechnique — Mathématiques, Volume 7  (2020), p. 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 : 2019-02-17
Accepted : 2019-10-09
Published online : 2019-11-08
DOI : https://doi.org/10.5802/jep.111
Classification:  37C40,  28D10
Keywords: Nilflows, time-changes, Ratner property, multiple mixing, disjointness
@article{JEP_2020__7__63_0,
     author = {Giovanni Forni and Adam Kanigowski},
     title = {Multiple mixing and disjointness for time changes of bounded-type Heisenberg nilflows},
     journal = {Journal de l'\'Ecole polytechnique --- Math\'ematiques},
     publisher = {\'Ecole polytechnique},
     volume = {7},
     year = {2020},
     pages = {63-91},
     doi = {10.5802/jep.111},
     language = {en},
     url = {https://jep.centre-mersenne.org/item/JEP_2020__7__63_0}
}
Forni, Giovanni; Kanigowski, Adam. 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/item/JEP_2020__7__63_0/

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