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

DOI10.5802/aif.2202zbMath1123.37001arXivmath/0503367OpenAlexW1643698954MaRDI QIDQ877530

Nikos Frantzikinakis, Emmanuel Lesigne, Máté Wierdl

Publication date: 24 April 2007

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503367

zbMATH Keywords

ergodic theorycombinatorial additive number theorymultiple recurrent setssets of \(k\)-recurrence

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Recurrences (11B37) Additive difference equations (39A10) General groups of measure-preserving transformations and dynamical systems (37A15) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items (7)

Some open problems on multiple ergodic averages ⋮ A generalization of van der Corput's difference theorem with applications to recurrence and multiple ergodic averages ⋮ Variations on topological recurrence ⋮ Nil Bohr-sets and almost automorphy of higher order ⋮ Random differences in Szemerédi's theorem and related results ⋮ Recurrence properties of sequences of integers ⋮ Powers of sequences and convergence of ergodic averages

Cites Work

• An ergodic Szemerédi theorem for commuting transformations
• Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
• Nonconventional ergodic averages and nilmanifolds
• The ergodic theoretical proof of Szemerédi’s theorem
• Universal characteristic factors and Furstenberg averages
• Weakly mixing PET
• Chromatic numbers of Cayley graphs on \(\mathbb Z\) and recurrence
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