Furstenberg, Harry Poincaré recurrence and number theory. (English) Zbl 0481.28013 Bull. Am. Math. Soc., New Ser. 5, 211-234 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 50 Documents MSC: 28D05 Measure-preserving transformations 54H20 Topological dynamics (MSC2010) 11B25 Arithmetic progressions 37A99 Ergodic theory Keywords:recurrence Citations:Zbl 0459.28023 PDFBibTeX XMLCite \textit{H. Furstenberg}, Bull. Am. Math. Soc., New Ser. 5, 211--234 (1981; Zbl 0481.28013) Full Text: DOI References: [1] L. Auslander, L. Green and F. Hahn, Flows on homogeneous spaces, Ann. of Math. Studies, No. 53, Princeton Univ. Press, Princeton, N. J., 1963. · Zbl 0099.39103 [2] George D. Birkhoff, Dynamical systems, With an addendum by Jurgen Moser. American Mathematical Society Colloquium Publications, Vol. IX, American Mathematical Society, Providence, R.I., 1966. [3] H. Furstenberg, Recurrence in ergodic theory and combinatorial number theory, Princeton University Press, Princeton, N.J., 1981. M. B. Porter Lectures. · Zbl 0459.28023 [4] H. Furstenberg and Y. Katznelson, An ergodic Szemerédi theorem for commuting transformations, J. Analyse Math. 34 (1978), 275 – 291 (1979). · Zbl 0426.28014 · doi:10.1007/BF02790016 [5] H. Furstenberg and B. Weiss, Topological dynamics and combinatorial number theory, J. Analyse Math. 34 (1978), 61 – 85 (1979). · Zbl 0425.54023 · doi:10.1007/BF02790008 [6] I. Schur, Über die Kongruenz x (mod p), Jahresber. Deutsch. Math.-Verein. 25(1916), 114-117. · JFM 46.0193.02 [7] E. Szemerédi, On sets of integers containing no \? elements in arithmetic progression, Acta Arith. 27 (1975), 199 – 245. Collection of articles in memory of Juriĭ Vladimirovič Linnik. · Zbl 0303.10056 [8] William A. Veech, Topological dynamics, Bull. Amer. Math. Soc. 83 (1977), no. 5, 775 – 830. · Zbl 0384.28018 [9] Hermann Weyl, Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), no. 3, 313 – 352 (German). · JFM 46.0278.06 · doi:10.1007/BF01475864 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.