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Approximately transitive (2) flows and transformations have simple spectrum

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Dynamical Systems

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References

  1. Auslander, L., Green, L., and Hahn, F., Flows on Homogeneous Spaces, Annals of Math. Studies, Princeton Univ. Press, (1963).

    Google Scholar 

  2. Ambrose, W., and Kakutani, S., Structure and continuity of measurable flows, Duke Math. J. 9, (1942), 25–42.

    Article  MathSciNet  MATH  Google Scholar 

  3. Connes, A., Feldman, J. and Weiss, B., An amenable equivalence relation is generated by a single transformation, Erg. Th. and Dyn. Sys., Vol. 1,4, (1981), 431–450.

    Article  MathSciNet  MATH  Google Scholar 

  4. Choksi, J., and M. Nadkarni, Baire category in spaces of measures, unitary operators, preprint (1986).

    Google Scholar 

  5. Connes, A., and Woods, E.J. Approximately transitive flows and ITPFI factors, Erg. Th. and Dyn. Sys., Vol. 5,2, (1985), 203–236.

    Article  MathSciNet  MATH  Google Scholar 

  6. Cornfeld, I., Fomin, S., and Sinai, Y., Ergodic Theory, Grund. 245, Springer-Verlag, (1982).

    Google Scholar 

  7. Dye, H., On groups of measure-preserving transformations, Amer. J. Math. 81, (1959), 119–159; II, Amer. J. Math 85, (1963), 551–576.

    Article  MathSciNet  MATH  Google Scholar 

  8. Ferenczi, S., Systémes de rang un gauche, Ann. Inst. Henri Poincaré, 21, No. 2, (1985), 177–186.

    MathSciNet  MATH  Google Scholar 

  9. Hamachi, T. and Osikawa, M., Ergodic groups of automorphisms and Krieger’s theorem, Sem. on Math. Sci. Keio Univ. 3, (1981).

    Google Scholar 

  10. Hawkins, J., Properties of ergodic flows associated to product odometers, to appear, Pac. Journal of Math.

    Google Scholar 

  11. Hawkins, J., and Woods, E.J. Approximately transitive diffeomorphisms of the circle, Proc. AMS, 90, No.2, (1984), 258–262.

    Article  MathSciNet  MATH  Google Scholar 

  12. Helson, H. and Parry, W., Cocycles and spectra, Arkiv. for Math., 16, No.2, (1978), 195–206.

    Article  MathSciNet  MATH  Google Scholar 

  13. Katok, A., Constructions in ergodic theory, to appear, Kirkhauser Progress in Math.

    Google Scholar 

  14. Katok, A., and Stepin, A., Approximations in ergodic theory, Russ. Math. Surv., 22, No. 5, (1967), 77–102.

    Article  MathSciNet  MATH  Google Scholar 

  15. Krieger, W., On ergodic flows and isomorphism of factors, Math. Ann. 223, (1976), 19–70.

    Article  MathSciNet  MATH  Google Scholar 

  16. Ornstein, D., Rudolph, D., and Weiss, B., Equivalence of measure-preserving transformations, Memoirs A.M.S., 37, No. 262, (1982).

    Google Scholar 

  17. Parasyuk, O., Horocycle flows on surfaces of constant negative curvature, Uspehi Mat. Nauk., 8, No. 3(55), (1953), 125–126, (in Russian).

    MathSciNet  Google Scholar 

  18. Parry, W., Spectral analysis of G-extensions of dynamical systems, Topology, 9, (1970), 217–224.

    Article  MathSciNet  Google Scholar 

  19. Ratner, M., Horocycle flows are loosely Bernoulli, Isr. J. Math., 31, (1978), 122–131.

    Article  MathSciNet  MATH  Google Scholar 

  20. Riley, G., Approximations and the spectral properties of measure-preserving group actions, Isr. J. Math., 33, No. 1 (1979), 9–31.

    Article  MathSciNet  MATH  Google Scholar 

  21. Robinson, Jr., E. A., Ergodic measure-preserving transformations with arbitrary finite spectral multiplicity, Invent. Math., 72, (1983), 299–314.

    Article  MathSciNet  MATH  Google Scholar 

  22. Sutherland, C., Notes on orbit equivalence; Krieger’s theorem, Lecture note series No.23, Univ. i Oslo, (1976).

    Google Scholar 

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James C. Alexander

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© 1988 Springer-Verlag

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Hawkins, J.M., Robinson, E.A. (1988). Approximately transitive (2) flows and transformations have simple spectrum. In: Alexander, J.C. (eds) Dynamical Systems. Lecture Notes in Mathematics, vol 1342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082836

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  • DOI: https://doi.org/10.1007/BFb0082836

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  • Print ISBN: 978-3-540-50174-9

  • Online ISBN: 978-3-540-45946-0

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