Skip to main content

Approximately transitive (2) flows and transformations have simple spectrum

Part of the Lecture Notes in Mathematics book series (LNM,volume 1342)

Keywords

  • Simple Spectrum
  • Constant Negative Curvature
  • Ergodic Transformation
  • Spectral Multiplicity
  • Finite Borel Measure

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  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.

    CrossRef  MathSciNet  Google Scholar 

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

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  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 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50174-9

  • Online ISBN: 978-3-540-45946-0

  • eBook Packages: Springer Book Archive