Hostname: page-component-7dd5485656-zlgnt Total loading time: 0 Render date: 2025-10-31T18:11:04.005Z Has data issue: false hasContentIssue false
  • English
  • Français

Uncountably many topological models for ergodic transformations

Published online by Cambridge University Press:  19 September 2008

S. Glasner  and
D. Rudolph
S. Glasner
Affiliation:
Tel Aviv University, Ramat Aviv, Israel;
D. Rudolph
Affiliation:
University of Maryland, College Park, MD 20742, USA
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.

Given a topological process (X, µ, T) where T is a homeomorphism of the compact metric space X which preserves the probability measure µ and is ergodic, we show that there exists an uncountable family {(Xi, µi, Ti)}i∈I of topological processes such that for every i, (Xi, µi, Ti) is measure-theoretically isomorphic to (X, µ, T) but for every i ≠ j, (Xi, µi, Ti) and (Xj, µj, Tj) are not almost topologically conjugate.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 2 , June 1984 , pp. 233 - 236
Copyright
Copyright © Cambridge University Press 1984

References

REFERENCES

[1]Denker, M. & Keane, M.. Almost topological dynamical systems. Israel J. Math. 34 (1979), 139–160.CrossRefGoogle Scholar
[2]Fiebig, U. R.. A return time invariant for finitary isomorphism. Ergod. Th. & Dynam. Sys. 4 (1984), 225–231.CrossRefGoogle Scholar
[3]Furstenberg, H.. Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions. J. d'Analyse Math. 31 (1977), 204–256.CrossRefGoogle Scholar