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Optimal lower bounds for multiple recurrence
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Donoso, Sebastian, Ngoc Le, Anh, Moreira, Joel and Sun, Wenbo (2019) Optimal lower bounds for multiple recurrence. Ergodic Theory and Dynamical Systems . doi:10.1017/etds.2019.72 (In Press)
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Official URL: https://doi.org/10.1017/etds.2019.72
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 > Mathematics | ||||||
| Journal or Publication Title: | Ergodic Theory and Dynamical Systems | ||||||
| Publisher: | Cambridge University Press | ||||||
| ISSN: | 0143-3857 | ||||||
| Official Date: | 7 October 2019 | ||||||
| Dates: |
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| Date of first compliant deposit: | 18 October 2019 | ||||||
| DOI: | 10.1017/etds.2019.72 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | In Press | ||||||
| Publisher Statement: | 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 |
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