Skip to main content
SpringerLink
Log in

Actions by automorphisms of commutative compact groups with a countablefold Lebesgue component in the spectrum

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature cited

  1. A. N. Kolmorogov, “A new metric invariant of transitive dynamical systems and of automorphisms of Lebesgue spaces,” Dokl. Akad. Nauk SSSR,119, No. 5, 861–864 (1958).

    Google Scholar 

  2. A. M. Vershik, “The spectral and metric isomorphism of certain normal dynamical systems,” Dokl. Akad. Nauk SSSR,144, No. 2, 255–257 (1962).

    Google Scholar 

  3. M. V. Girsanov, “The spectrum of dynamical systems generated by a stationary Gaussian process,” Dokl. Akad. Nauk SSSR,119, No. 5, 851–853 (1958).

    Google Scholar 

  4. V. I. Oseledets, “The spectrum of ergodic automorphisms,” Dokl. Akad. Nauk SSSR,168, No. 5, 1009–1011 (1966).

    Google Scholar 

  5. A. M. Stepin, “The spectral properties of typical dynamical systems,” Izv. Akad. Nauk SSSR Ser. Mat.,50, No. 4, 801–834 (1986).

    Google Scholar 

  6. A. M. Vershik, I. P. Kornfel'd and Ya. G. Sinai, “General ergodic theory of transformation groups with invariant measure,” in: Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Vol. 2, VINITI (1985) pp. 5–111.

  7. A. A. Kirillov, “Dynamical systems, factors and representations of groups,” Usp. Mat. Nauk,22, No. 5, 67–80 (1967).

    Google Scholar 

  8. S. Ulam, A Collection of Mathematical Problems, Interscience, New York (1960).

    Google Scholar 

  9. I. P. Kornfel'd, Ya. G. Sinai, and S. V. Fomin, Ergodic Theory [in Russian], Nauka, Moscow (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    O. N. Ageev

Authors
  1. O. N. Ageev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 49, No. 2, pp. 14–22, February, 1991.

In conclusion, the author conveys gratitude to A. M. Stepin for stating the problem and to R. I. Grigorchuk for some useful advice on improving the contents of the text.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ageev, O.N. Actions by automorphisms of commutative compact groups with a countablefold Lebesgue component in the spectrum. Mathematical Notes of the Academy of Sciences of the USSR 49, 124–130 (1991). https://doi.org/10.1007/BF01137540

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01137540

Keywords

Search

Navigation