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Book Review
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Full text of review:
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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.
- 1.
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 (24 #A3266)
- 2.
J.
Cigler, On a theorem of H. Weyl, Compositio Math.
21 (1969), 151–154. MR 0245530
(39 #6836)
- 3.
Harry
Furstenberg, Stationary processes and prediction theory,
Annals of Mathematics Studies, No. 44, Princeton University Press,
Princeton, N.J., 1960. MR 0140151
(25 #3573)
- 4.
H.
Furstenberg, Strict ergodicity and transformation of the
torus, Amer. J. Math. 83 (1961), 573–601. MR 0133429
(24 #A3263)
- 5.
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
(84b:28016), http://dx.doi.org/10.1090/S0273-0979-1982-15052-2
- 6.
F.
J. Hahn, On affine transformations of compact abelian groups,
Amer. J. Math. 85 (1963), 428–446. MR 0155956
(27 #5889)
- 7.
F.
J. Hahn, Skew product transformations and the algebras generated by
𝑒𝑥𝑝(𝑝(𝑛)), Illinois J. Math.
9 (1965), 178–190. MR 0174989
(30 #5177)
- 8.
A.
G. Postnikov, Ergodic problems in the theory of congruences and of
Diophantine approximations, Proceedings of the Steklov Institute of
Mathematics, No. 82 (1966). Translated from the Russian by B. Volkmann,
American Mathematical Society, Providence, R.I., 1967. MR 0214560
(35 #5409)
- 9.
William
A. Veech, Topological dynamics, Bull. Amer. Math. Soc. 83 (1977), no. 5, 775–830. MR 0467705
(57 #7558), http://dx.doi.org/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 133432
- 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:
http://dx.doi.org/10.1090/S0273-0979-1986-15451-0
PII:
S 0273-0979(1986)15451-0
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