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Poincaré recurrence and number theory. (English) Zbl 0481.28013


MSC:

28D05 Measure-preserving transformations
54H20 Topological dynamics (MSC2010)
11B25 Arithmetic progressions
37A99 Ergodic theory

Keywords:

recurrence

Citations:

Zbl 0459.28023
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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
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