Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-28T19:22:00.747Z Has data issue: false hasContentIssue false
  • English
  • Français

On generic points in the Cartesian square of Chacón's transformation

Published online by Cambridge University Press:  19 September 2008

A. Del Junco  and
M. Keane
A. Del Junco
Affiliation:
Mathematics Department, University of Toronto, Toronto M5S 1A1, Canada
M. Keane
Affiliation:
Technische Hogeschool Delft, Afdeling Wiskunde, 2628 BL Delft, The, Netherlands
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.

We give an example of a compact metric space X and a strictly ergodic homeomorphism T of X with invariant probability μ such that for every x ∈ X the set is not generic for μ × μ} is countable.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 1 , March 1985 , pp. 59 - 69
Copyright
Copyright © Cambridge University Press 1985

References

REFERENCES

[1]Furstenberg, H., Keynes, H. & Shapiro, L.. Prime flows in topological dynamics. Israel J. Math. 14 (1973), 26–38.CrossRefGoogle Scholar
[2]Glasner, S.. Quasifactors in ergodic theory. Israel. Math. 45 (1983), 198–208.CrossRefGoogle Scholar
[3]Glasner, S.. Absolutely extremal points in minimal flows. Preprint.Google Scholar
[4]del Junco, A.. A family of counterexamples in ergodic theory. Israel J. Math. 44 (1983) 160–188.CrossRefGoogle Scholar
[5]del Junco, A.. Prime systems in ergodic theory and topological dynamics. Lecture notes, Technische Hogeschool Delft.Google Scholar
[6]del Junco, A. and Rudolph, D.. To appear.Google Scholar
[7]del Junco, A., Rahe, M. & Swanson, L.. Chacón's automorphism has minimal self-joinings. J. d' Analyse Math. 37 (1980), 276–284.CrossRefGoogle Scholar
[8]Markley, N.. Topological minimal self-joinings. Ergod. Th. & Dynam. Sys. 3 (1983), 579–599.CrossRefGoogle Scholar
[9]Ratner, M.. Joinings of horocycle flows. Preprint.Google Scholar
[10]Rudolph, D.. An example of a measure-preserving map with minimal self-joinings and applications. J. d' Analyse Math. 35 (1979), 97–122.Google Scholar