Nous étudions les reparamétrisations des flots nilpotents de Heisenberg de type borné sur une variété nilpotente de Heisenberg . Nous montrons que, pour des fonctions positives (espace de Sobolev) avec , toute reparamétrisation non triviale 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 , avec et pour tous , , les flots et 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.
We study time changes of bounded type Heisenberg nilflows acting on the Heisenberg nilmanifold . We show that for every positive , , every non-trivial time change enjoys the Ratner property. As a consequence, every mixing time change is mixing of all orders. Moreover, we show that for every , and every , , and are disjoint. As a consequence, Sarnak conjecture on Möbius disjointness holds for all such time changes.
Accepté le :
Publié le :
DOI : 10.5802/jep.111
Keywords: Nilflows, time-changes, Ratner property, multiple mixing, disjointness
Mot clés : Flots nilpotents, reparamétrisations, propriété de Ratner
@article{JEP_2020__7__63_0, author = {Forni, Giovanni and Kanigowski, Adam}, title = {Multiple mixing and disjointness for time changes of bounded-type {Heisenberg} nilflows}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {63--91}, publisher = {Ecole polytechnique}, volume = {7}, year = {2020}, doi = {10.5802/jep.111}, zbl = {07128377}, mrnumber = {4033750}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jep.111/} }
TY - JOUR AU - Forni, Giovanni AU - Kanigowski, Adam TI - Multiple mixing and disjointness for time changes of bounded-type Heisenberg nilflows JO - Journal de l’École polytechnique — Mathématiques PY - 2020 SP - 63 EP - 91 VL - 7 PB - Ecole polytechnique UR - http://archive.numdam.org/articles/10.5802/jep.111/ DO - 10.5802/jep.111 LA - en ID - JEP_2020__7__63_0 ER -
%0 Journal Article %A Forni, Giovanni %A Kanigowski, Adam %T Multiple mixing and disjointness for time changes of bounded-type Heisenberg nilflows %J Journal de l’École polytechnique — Mathématiques %D 2020 %P 63-91 %V 7 %I Ecole polytechnique %U http://archive.numdam.org/articles/10.5802/jep.111/ %R 10.5802/jep.111 %G en %F 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, Tome 7 (2020), pp. 63-91. doi : 10.5802/jep.111. http://archive.numdam.org/articles/10.5802/jep.111/
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