{"title":"Distinguishing sets of strong recurrence from van der Corput sets","authors":"Andreas Mountakis","doi":"10.1007/s11856-024-2644-7","DOIUrl":null,"url":null,"abstract":"<p>Sets of recurrence, which were introduced by Furstenberg, and van der Corput sets, which were introduced by Kamae and Mendés France, as well as variants thereof, are important classes of sets in Ergodic Theory. In this paper, we construct a set of strong recurrence which is not a van der Corput set. In particular, this shows that the class of enhanced van der Corput sets is a proper subclass of sets of strong recurrence. This answers some questions asked by Bergelson and Lesigne.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Israel Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11856-024-2644-7","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Sets of recurrence, which were introduced by Furstenberg, and van der Corput sets, which were introduced by Kamae and Mendés France, as well as variants thereof, are important classes of sets in Ergodic Theory. In this paper, we construct a set of strong recurrence which is not a van der Corput set. In particular, this shows that the class of enhanced van der Corput sets is a proper subclass of sets of strong recurrence. This answers some questions asked by Bergelson and Lesigne.
期刊介绍：
The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.
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