Ruzsa's problem on sets of recurrence

DOI10.1007/BF02787258zbMath0643.10045OpenAlexW1974504121MaRDI QIDQ1101485

Jean Bourgain

Publication date: 1987

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02787258

zbMATH Keywords

difference setsPoincaré setintersectivityrecurrent setapproximativitycorrelative setscorrelativityexistence of Poincaré sequences of integers which are not van der Corput sets

Mathematics Subject Classification ID

Ergodic theory of linear operators (47A35) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Additive bases, including sumsets (11B13) Probabilistic theory: distribution modulo (1); metric theory of algorithms (11K99) Measure-theoretic ergodic theory (28D99)

Related Items (16)

Dynamical Systems and Uniform Distribution of Sequences ⋮ On random perturbation of some intersective sets. ⋮ Application of Banach limits to the study of sets of integers ⋮ Ergodic characterization of van der Corput sets ⋮ On van der Corput property of shifted primes ⋮ Some results on Poincaré sets ⋮ Uniform distribution of prime powers and sets of recurrence and van der Corput sets in \(\mathbb{Z}^k\) ⋮ Difference sets and positive exponential sums. I: General properties ⋮ On Szemerédi’s theorem with differences from a random set ⋮ A note on Euclidean Ramsey theory and a construction of Bourgain ⋮ Van der Corput sets with respect to compact groups ⋮ The construction of a set of recurrence which is not a set of strong recurrence ⋮ Random differences in Szemerédi's theorem and related results ⋮ On asymptotic distribution on the \({\mathbf a}\)-adic integers ⋮ MULTIDIMENSIONAL VAN DER CORPUT SETS AND SMALL FRACTIONAL PARTS OF POLYNOMIALS ⋮ Problems and Results on Intersective Sets

Cites Work

• Ensembles intersectifs et récurrence de Poincaré. (Intersective sets and Poincaré recurrence)
• Van der Corput's difference theorem
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