Journal of Dynamical and Control Systems

, Volume 5, Issue 1, pp 149–152 | Cite as

On Ergodic Transformations with Homogeneous Spectrum

  • O.N. Ageev


Rokhlin's problem on the existence of an ergodic transformation having a homogeneous spectrum of a finite multiplicity is solved. Katok's question about the spectral multiplicity function of Cartesian powers for a generic transformations is also answered.

Homogeneous spectrum ergodic theory 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. del Junco, A simple measure-preserving transformation with trivial centralizer. Basic J. Math. 79 (1978), No. 2, 357–362.Google Scholar
  2. 2.
    A. B. Katok and A. M. Stepin, Metrical propertys of measure preserving homeomorphisms. (Russian) Math. Surv, 25, (1970), 193–220.Google Scholar
  3. 3.
    A. B. Katok, Constructions in ergodic theory. Unpublished lecture notes.Google Scholar
  4. 4.
    O. N. Ageev, The spectral type of the rearrangement T α,β. Mat. Sb. 188 (1997), 1119–1152.Google Scholar
  5. 5.
    G. R. Goodson and M. Leman'czyk, Transformations conjugate to their inverses have even essential values. Proc. Am. Math. Soc. 124 (1996), 2703–2710.Google Scholar
  6. 6.
    A. M. Stepin, Les spectres des systemes dynamique. In: Actes, Congres. Intern. Math. 2 (1970), 941–946.Google Scholar

Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • O.N. Ageev
    • 1
  1. 1.Department of MathematicsMoscow State Technical UniversityMoscow

Personalised recommendations