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A family of counterexamples in ergodic theory. (English) Zbl 0522.28012

28D05 Measure-preserving transformations
54H20 Topological dynamics (MSC2010)
Full Text: DOI
[1] J. Aaronson and M. Keane,The visits to zero of some deterministic random walks, preprint. · Zbl 0489.60006
[2] R. V. Chacón,Transformations having continuous spectrum, J. Math. Mech.16 (1966), 399–415. · Zbl 0154.30602
[3] R. V. Chacón,Weakly mixing transformations which are not strongly mixing, Proc. Am. Math. Soc.22 (1969), 559–562. · Zbl 0186.37203 · doi:10.1090/S0002-9939-1969-0247028-5
[4] H. Furstenberg, H Keynes and L. Shapiro,Prime flows in topological dynamics, Isr. J. Math.14 (1973), 26–38. · Zbl 0264.54030 · doi:10.1007/BF02761532
[5] A. del Junco,A simple measure-preserving transformation with trivial centralizer, Pac. J. Math.79 (1978), 357–362. · Zbl 0368.28019
[6] A. del Junco and D. Rudolph,Universally disjoint measure-preserving systems, to appear.
[7] A. del Junco, M. Rahe and L. Swanson,Chacón’s automorphism has minimal self-joinings, J. Analyse Math.37 (1980), 276–284. · Zbl 0445.28014 · doi:10.1007/BF02797688
[8] S. Kakutani,Examples of ergodic measure-preserving transformations which are weakly mixing but not strongly mixing, Springer Lecture Notes in Math.318 (1973), 143–149. · Zbl 0267.28008 · doi:10.1007/BFb0061731
[9] A. B. Katok, Ya. G. Sinai and A. M. Stepin,Theory of dynamical systems and general transformation groups with invariant measure, J. Sov. Math.7 (1977), 974–1065. · Zbl 0399.28011 · doi:10.1007/BF01223133
[10] M. Keane,Irrational rotations and quasi-ergodic measures, Publ. des Séminaires de Math. (Fasc. I Prob.), Rennes, 1970–71.
[11] D. S. Ornstein,On the root problem in ergodic theory, Proc. Sixth Berkeley Symp. Math. Stat. Prob. Vol. II, University of California Press, 1967, pp. 347–356.
[12] D. Rudolph,An example of a measure-preserving map with minimal self-joinings, and applications, J. Analyse Math.35 (1979), 97–122. · Zbl 0446.28018 · doi:10.1007/BF02791063
[13] W. Weech,Strict ergodicity in zero-dimensional dynamical systems and the Kronecker-Weyl theorem mod 2, Trans. Am. Math. Soc.140 (1969), 1–33. · Zbl 0201.05601
[14] W. Veech,Well distributed sequences of integers, Trans. Am. Math. Soc.161 (1971), 63–70. · Zbl 0229.10019 · doi:10.1090/S0002-9947-1971-0285497-9
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