Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T05:12:40.385Z Has data issue: false hasContentIssue false
  • English
  • Français

Compact subgroups in the centralizer of natural factors of an ergodic group extension of a rotation determine all factors

Published online by Cambridge University Press:  19 September 2008

Mariusz Lemańczyk  and
Mieczyslaw K. Mentzen
Mariusz Lemańczyk
Affiliation:
Institute of Mathematics, Nicholas Copernicus University, ul. Chopina 12/18, 87–100 Toruń, Poland
Mieczyslaw K. Mentzen
Affiliation:
Institute of Mathematics, Nicholas Copernicus University, ul. Chopina 12/18, 87–100 Toruń, Poland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For ergodic group extensions of transformations with discrete spectra it is proved that each invariant sub-σ-algebra is determined by a compact subgroup in the centralizer of a natural factor.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 4 , December 1990 , pp. 763 - 776
Copyright
Copyright © Cambridge University Press 1990

References

REFERENCES

[1]Anzai, H.. Ergodic skew-product transformations on the torus. Osaka J. Math. 3 (1951), 83–99.Google Scholar
[2]Hahn, F. & Parry, W.. Some characteristic properties of dynamical systems with quasi-discrete spectra. Math. Syst. Th. 2 (1968), 179–190.CrossRefGoogle Scholar
[3]del Junco, A. & Rudolph, D.. A rank-one, rigid, simple prime map. Ergod. Th. Dynam. & Sys. 1 (1987), 229–247.CrossRefGoogle Scholar
[4]del Junco, A. & Rudolph, D.. On ergodic actions whose self-joinings are graphs. Ergod. Th. & Dynam. Sys. 7 (1987), 531–557.CrossRefGoogle Scholar
[5]Keynes, H. B. & Newton, D.. The structure of ergodic measures for compact group extensions. Isr. J. Math. 18 (4) (1974), 363–389.CrossRefGoogle Scholar
[6]Lemańczyk, M. & Liardet, P.. Coalescence of Anzai skew products (to appear).Google Scholar
[7]Newton, D.. On canonical factors of ergodic dynamical systems. J. London Math. Soc. 2, 19 (1979), 129–136.CrossRefGoogle Scholar
[8]Parry, W.. Compact abelian group extensions of discrete dynamical systems. Z. Wahr. Venv. Geb. 13 (1969), 95–113.CrossRefGoogle Scholar
[9]Rudolph, D.. An example of measure-preserving map with minimal self-joinings, and applications. J. d'Analyse Math. 35 (1979), 97–122.CrossRefGoogle Scholar
[10]Varadarajan, V. S.. Geometry of Quantum Theory. Vol. II, Van Nostrand Reinhold, New York (1970).Google Scholar
[11]Veech, W. A.. A criterion for a process to be prime. Monatsh. Math. 94 (1982), 335–341.CrossRefGoogle Scholar