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A map with topological minimal self-joinings in the sense of del Junco

Published online by Cambridge University Press:  19 September 2008

Jonathan L. King
Jonathan L. King
Affiliation:
Mathematics Department, University of California, Berkeley CA 94720, USA
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Abstract

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Andrés del Junco has proposed a definition of topological minimal self-joinings intended to parallel Dan Rudolph's measure-theoretic concept. By means of a rank-two ‘cutting and stacking’, this article constructs the first example of a system (a subshift) satisfying his proposed definition of 2-fold topological minimal self-joinings.

The second part of the article shows that 2-fold topological minimal self-joinings does not imply 3-fold and that no map has 4-fold topological minimal self-joinings. This latter result follows from a generalization of a theorem of Schwartzman.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 4 , December 1990 , pp. 745 - 761
Copyright
Copyright © Cambridge University Press 1990

References

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