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Poincaré recurrence and number theory
Author(s):
Harry
Furstenberg
Journal:
Bull. Amer. Math. Soc.
5
(1981),
211-234.
MSC (1980):
Primary 05A05, 28D05, 58F11;
Secondary 10A99
Link to commentary:
Bull. Amer. Math. Soc., 48 (2011), no. 4, to appear.
MathSciNet review:
628658
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Additional information
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.
- 2.
- G. D. Birkhoff, Dynamical systems, Amer. Math. Soc. Colloq. Publ., vol. 9, Amer. Math. Soc., Providence, R. L, 1927. MR 209095
- 3.
- H. Furstenberg, Recurrence in ergodic theory and combinatorial number theory, Princeton Univ. Press, Princeton, N. J., 1981. MR 603625
- 4.
- H. Furstenberg and Y. Katznelson, An ergodic Szemerédi theorem for commuting transformations, J. d'Analyse Math. 34 (1978), 275-291. MR 531279
- 5.
- H. Furstenberg and B. Weiss, Topological dynamics and combinatorial number theory, J. d'Analyse Math. 34 (1978), 61-85. MR 531271
- 6.
- I. Schur, Über die Kongruenz x (mod p), Jahresber. Deutsch. Math.-Verein. 25(1916), 114-117.
- 7.
- E. Szemerédi, On sets of integers containing no k elements in arithmetic progression, Acta Arith. 27 (1975), 199-245. MR 369312
- 8.
- W. A. Veech, Topological dynamics, Bull. Amer. Math. Soc. 85 (1977), 775-830. MR 467705
- 9.
- H. Weyl, Über die Gleichverteilung von Zahlen mod Eins, Math. Ann. 77 (1916), 313-352. MR 1511862
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Additional Information:
DOI:
10.1090/S0273-0979-1981-14932-6
PII:
S 0273-0979(1981)14932-6
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