Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-30T22:23:09.471Z Has data issue: false hasContentIssue false
  • English
  • Français

Topological minimal self-joinings

Published online by Cambridge University Press:  19 September 2008

Nelson G. Markley
Nelson G. Markley
Affiliation:
Department of Mathematics, 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.

There is an interesting duality between some of the concepts of ergodic theory and those of topological dynamics. This paper is a first attempt at developing a topological analogue to the measure-theoretic notion of a transformation having minimal self-joinings. The main problem is to understand the dynamics of the composition of a cartesian product of powers of a transformation having topological minimal self-joinings with a compact permutation of the coordinates. Most of the results are about the minimal subsets of such a composition.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 3 , Issue 4 , December 1983 , pp. 579 - 599
Copyright
Copyright © Cambridge University Press 1983

References

REFERENCES

[1]Chacon, R. V.. Weakly mixing transformations which are not strongly mixing. Proc. Amer. Math. Soc. 22 (1969), 559–562.CrossRefGoogle Scholar
[2]del Junco, A.. A family of counter-examples in ergodic theory. Preprint.Google Scholar
[3]del Junco, A., Rahe, M. & Swanson, L., Chacon's automorphism has minimal self-joinings. J. Analyse Math. 37 (1980), 276–284.CrossRefGoogle Scholar
[4]Ellis, R.. Lectures on Topological Dynamics. W. A. Benjamin: New York, 1969.Google Scholar
[5]Furstenberg, H., Keynes, H. & Shapiro, L.. Prime flows in topological dynamics. Israel J. Math. 14 (1973), 26–38.CrossRefGoogle Scholar
[6]Keynes, H.. The structure of weakly mixing minimal transformation groups. Illinois J. Math. 15 (1971), 475–489.CrossRefGoogle Scholar
[7]Keynes, H. & Newton, D.. Real prime flows. Trans. Amer. Math. Soc. 217 (1976), 237–255.CrossRefGoogle Scholar
[8]Markley, N.. Characteristic sequences. Recent Advances in Topological Dynamics. Lecture Notes in Mathematics vol. 318. Springer-Verlag: Berlin, 1972.Google Scholar
[9]Rudolph, D.. An example of a measure preserving map with minimal self-joinings, and applications. J. Analyse Math. 35 (1979), 97–122.CrossRefGoogle Scholar