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Mixing properties of substitutions. (English) Zbl 0352.28007


MSC:

28D05 Measure-preserving transformations
54H20 Topological dynamics (MSC2010)
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References:

[1] Chacon, R. V., Transformations having continuous spectrum, J. Math. Mech., 16, 399-415 (1966) · Zbl 0154.30602
[2] Coven, E. M.; Keane, M., The structure of substitution minimal sets, Trans. Amer. Math. Soc., 162, 89-102 (1971) · Zbl 0205.28303
[3] Dekking, F.M.: The spectrum of dynamical systems arising from substitutions of constant length. Preprint (1977)
[4] Dekking, F.M., Keane, M., Michel, P.: Substitutions. Seminar manuscript, Rennes (1977) · Zbl 1525.68104
[5] Friedman, N. A., Introduction to ergodic theory (1970), New York: Van Nostrand-Reinholt, New York · Zbl 0212.40004
[6] Goodman, S., Marcus, B.: Topological mixing of higher degrees. Preprint (1977) · Zbl 0408.54028
[7] Gottschalk, W., Hedlund, G.A.: Topological dynamics. Amer. Math. Soc. Colloq. Publ. Vol. 36, Providence (1955) · Zbl 0067.15204
[8] Halmos, P. R., Lectures on ergodic theory (1956), New York: Chelsea, New York · Zbl 0073.09302
[9] Jacobs, K.; Keane, M., 0-1-Sequences of Toeplitz type, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 13, 123-131 (1969) · Zbl 0195.52703
[10] Kakutani, S., Strictly ergodic symbolic dynamical systems, Proc. VI Berk. Sympos. Math. Statist. Probab., II, 319-326 (1972) · Zbl 0262.28014
[11] Kakutani, S., Examples of ergodic measure preserving transformations which are weakly mixing but not strongly mixing, SLN, 318, 143-149 (1972) · Zbl 0267.28008
[12] Michel, P., Stricte ergodicité d’ensembles minimaux de substitutions, C.R. Acad. Sci. Paris Sér. A-B, 278, 811-813 (1974) · Zbl 0274.60028
[13] Neveu, J., Sur les suites de Toeplitz, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 13, 132-134 (1969) · Zbl 0195.52801
[14] Petersen, K. E., A topologically strongly mixing symbolic minimal set, Trans. Amer. Math. Soc., 148, 603-612 (1970) · Zbl 0194.55001
[15] Petersen, K. E.; Shapiro, L., Induced Flows, Trans. Amer. Math. Soc., 177, 375-389 (1973) · Zbl 0229.54036
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