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Optimal lower bounds for multiple recurrence

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Donoso, Sebastian, Ngoc Le, Anh, Moreira, Joel and Sun, Wenbo (2021) Optimal lower bounds for multiple recurrence. Ergodic Theory and Dynamical Systems, 41 (2). pp. 379-407. doi:10.1017/etds.2019.72

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Official URL: https://doi.org/10.1017/etds.2019.72

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Abstract

Let be an ergodic measure-preserving system, let and let . We study the largeness of sets of the form for various families of sequences . For and , we show that has positive density if , where satisfies or and denotes the th prime; or when is a certain Hardy field sequence. If is ergodic for some , then, for all , is syndetic if . For , where are distinct integers, we show that can be empty for , and, for , we found an interesting relation between the largeness of and the abundance of solutions to certain linear equations in sparse sets of integers. We also provide some partial results when the are distinct polynomials.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Ergodic theory, Nilpotent groups, Isomorphisms (Mathematics)
Journal or Publication Title: Ergodic Theory and Dynamical Systems
Publisher: Cambridge University Press
ISSN: 0143-3857
Official Date: February 2021
Dates:
DateEvent
February 2021Published
7 October 2019Available
19 August 2019Accepted
Volume: 41
Number: 2
Page Range: pp. 379-407
DOI: 10.1017/etds.2019.72
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): This article has been published in a revised form in Ergodic Theory and Dynamical Systems [http://doi.org/10.1017/etds.2019.72. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © copyright holder.
Access rights to Published version: Restricted or Subscription Access
Copyright Holders: © Cambridge University Press, 2019
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
11160061Fondo Nacional de Desarrollo Científico y Tecnológicohttp://viaf.org/viaf/133259425
DMS-1700147National Science Foundationhttp://dx.doi.org/10.13039/501100008982

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