Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
MathSciNet review:
1567581
Full text of review:
PDF
This review is available free of charge.
Book Information:
Author:
H. Furstenberg
Title:
Recurrence in ergodic theory and combinatorial number theory
Additional book information:
Princeton Univ. Press, 1981, vii + 199 pp., $25.00. ISBN 0-691-08269-3.
N. M. Akuliničev, On a dynamical system related to the distribution of the fractional parts of a second-degree polynomial, Dokl. Akad. Nauk SSSR 143 (1962), 503–505 (Russian). MR 0133432
J. Cigler, On a theorem of H. Weyl, Compositio Math. 21 (1969), 151–154. MR 245530
Harry Furstenberg, Stationary processes and prediction theory, Annals of Mathematics Studies, No. 44, Princeton University Press, Princeton, N.J., 1960. MR 0140151
H. Furstenberg, Strict ergodicity and transformation of the torus, Amer. J. Math. 83 (1961), 573–601. MR 133429, DOI 10.2307/2372899
H. Furstenberg, Y. Katznelson, and D. Ornstein, The ergodic theoretical proof of Szemerédi’s theorem, Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 3, 527–552. MR 670131, DOI 10.1090/S0273-0979-1982-15052-2
F. J. Hahn, On affine transformations of compact abelian groups, Amer. J. Math. 85 (1963), 428–446. MR 155956, DOI 10.2307/2373133
F. J. Hahn, Skew product transformations and the algebras generated by $\textrm {exp}(p(n))$, Illinois J. Math. 9 (1965), 178–190. MR 174989
A. G. Postnikov, Ergodic problems in the theory of congruences and of Diophantine approximations, Proceedings of the Steklov Institute of Mathematics, No. 82 (1966), American Mathematical Society, Providence, R.I., 1967. Translated from the Russian by B. Volkmann. MR 0214560
William A. Veech, Topological dynamics, Bull. Amer. Math. Soc. 83 (1977), no. 5, 775–830. MR 467705, DOI 10.1090/S0002-9904-1977-14319-X
- 1.
- N. M. Akulsničev, On a dynamical system related to the distribution of the fractional parts of second-degree polynomials, Dokl. Akad. Nauk SSR 143 (1962), 503-505; English transl. Soviet Math. Dokl. 3 (1962), 405-407. MR 0133432
- 2.
- J. Cigler, On a theorem of H. Weyl, Compositio Math. 21 (1969), 151-154. MR 245530
- 3.
- H. Furstenberg, Stationary processes and prediction theory, Ann. of Math. Studies No. 44, Princeton Univ. Press, Princeton, N.J., 1960. MR 140151
- 4.
- H. Furstenberg, Strict ergodicity and transformations of the torus, Amer. J. Math. 83 (1961), 573-601. MR 133429
- 5.
- H. Furstenberg, Y. Katznelson and D. Ornstein, The ergodic theoretical proof of Szemerédi's theorem, Bull. Amer. Math. Soc. 7 (1982), 527-552. MR 670131
- 6.
- F. J. Hahn, On affine transformations of compact abelian groups, Amer. J. Math. 85 (1963), 428-446. Erratum 86 (1964). MR 155956
- 7.
- F. J. Hahn, Skew product transformations and the algebras generated by exp(p(n)), Illinois J. Math. 9 (1965), 178-190. MR 174989
- 8.
- A. G. Postnikov, Ergodic problems in the theory of congruences and of diophantine approximations, Trudy Mat. Inst. Steklov 82 (1966); English transl. Proc. Steklov Inst. Math. 82 (1967). MR 214560
- 9.
- William A. Veech, Topological dynamics, Bull. Amer. Math. Soc. 83 (1977), 775-830. MR 467705
Review Information:
Reviewer:
Karl Petersen
Journal:
Bull. Amer. Math. Soc.
14 (1986), 305-309
DOI:
https://doi.org/10.1090/S0273-0979-1986-15451-0
