Sets of transfer times with small densities
[Ensembles de temps de transfert avec petites densités]
Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 311-329.

Dans cet article, nous introduisons et discutons plusieurs notions de doublement pour des actions préservant la mesure sur un groupe abélien dénombrable G. Notre résultat principal caractérise les actions 2-doublantes et peut être vu comme une extension de nature ergodique de certains théorèmes de densité classiques pour les sommes d’ensembles par Kneser. Tous nos résultats sont optimaux et sont nouveaux déjà pour le cas où G=(,+).

In this paper we introduce and discuss various notions of doubling for measure-preserving actions of a countable abelian group G. Our main result characterizes 2-doubling actions, and can be viewed as an ergodic-theoretical extension of some classical density theorems for sumsets by Kneser. All of our results are completely sharp and they are new already in the case when G=(,+).

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DOI : https://doi.org/10.5802/jep.147
Classification : 37A44,  28D05,  11B13
Mots clés : Temps de retour, théorèmes inverses, sommes d’ensembles
Michael Björklund 1 ; Alexander Fish 2 ; Ilya D. Shkredov 3

1. Department of Mathematics, Chalmers University Chalmers Tvärgata 3, SE-412 96 Gothenburg, Sweden
2. The School of Mathematics and Statistics, Faculty of Science, The University of Sydney NSW 2006, Sydney, Australia
3. Steklov Mathematical Institute ul. Gubkina 8, 119991 Moscow, Russia
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Michael Björklund; Alexander Fish; Ilya D. Shkredov. Sets of transfer times with small densities. Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 311-329. doi : 10.5802/jep.147. https://jep.centre-mersenne.org/articles/10.5802/jep.147/

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