Sets of k-recurrence but not (k+1)-recurrence

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dc.creatorFrantzikinakis, N.
dc.creatorLesigne, E.
dc.creatorWierdl, M.
dc.date2005-03-17
dc.date2005-04-05
dc.date.accessioned2026-07-07T05:18:05Z
dc.date.available2026-07-07T05:18:05Z
dc.descriptionFor every $k\in \mathbb{N}$, we produce a set of integers which is $k$-recurrent but not $(k+1)$-recurrent. This extends a result of Furstenberg who produced a 1-recurrent set which is not 2-recurrent. We discuss a similar result for convergence of multiple ergodic averages. Finally, we also point out a combinatorial consequence related to Szemer\' edi's theorem.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/math/0503367
dc.identifierhttp://arxiv.org/abs/math/0503367
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74539
dc.subjectDynamical Systems
dc.subjectCombinatorics
dc.subject37A45, 28D05
dc.titleSets of k-recurrence but not (k+1)-recurrence
dc.typetext

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