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Transactions of the American Mathematical Society

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Ergodic measure preserving transformations with quasi-discrete spectrum


Author: James B. Robertson
Journal: Trans. Amer. Math. Soc. 190 (1974), 301-311
MSC: Primary 28A65
DOI: https://doi.org/10.1090/S0002-9947-1974-0344419-5
MathSciNet review: 0344419
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Abstract: It is shown that an ergodic measure preserving transformation with quasi-discrete spectrum is conjugate to: (a) the skew-product of an ergodic measure preserving transformation with discrete spectrum and a measurable family of totally ergodic measure preserving transformations with quasi-discrete spectrum; (b) a factor of the direct product of an ergodic measure preserving transformation with discrete spectrum and a totally ergodic measure preserving transformation with quasi-discrete spectrum. Sufficient conditions are given to insure that an ergodic measure preserving transformation with quasi-discrete spectrum is conjugate to the direct product of an ergodic measure preserving transformation with discrete spectrum and a totally ergodic measure preserving transformation with quasi-discrete spectrum.


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  • [1] L, Abramov, Metric automorphisms with quasi-discrete spectrum, Izv. Akad. Nauk SSSR Ser. Mat. 26 (1962), 513-530; English transl., Amer. Math. Soc. Transl. (2) 39 (1964), 37-56. MR 26 #606. MR 0143040 (26:606)
  • [2] F. Hahn and W. Parry, Minimal dynamical systems with quasi-discrete spectrum, J. London Math. Soc. 40 (1965), 309-323. MR 30 #5292. MR 0175107 (30:5292)
  • [3] -, Some characteristic properties of dynamical systems with quasi-discrete spectra, Math. Systems Theory 2 (1968), 179-190. MR 37 #6435. MR 0230877 (37:6435)
  • [4] P. Halmos, Lectures on ergodic theory, Publ. Math. Soc. Japan, no. 3, Math. Soc. of Japan, Tokyo, 1956. MR 20 #3958. MR 0097489 (20:3958)
  • [5] A. Kuroš, Theory of groups, GITTL, Moscow, 1953; English transl. of 2nd ed., Vol. I, Chelsea, New York, 1955. MR 15, 501; 17, 124.
  • [6] H. Weyl, Uber die Gleichverteilung von Zohlen mod. Eins, Math. Ann. 77 (1916), 313-352. MR 1511862

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0344419-5
Keywords: Measure preserving, totally ergodic, quasi-discrete spectrum, quasi-eigenvalues
Article copyright: © Copyright 1974 American Mathematical Society

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