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Minimal sets on tori

Published online by Cambridge University Press:  19 September 2008

Daniel Berend
Daniel Berend
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90024, USA
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Abstract

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Let Σ be a commutative semigroup of continuous endomorphisms of the r-dimensional torus. Generalizing a result of Furstenberg dealing with the circle group, necessary and sufficient conditions are given here for Σ to possess the following property: Any Σ-minimal set consists of torsion elements. Semigroups not having this property are shown to admit minimal sets of positive Hausdorff dimension.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 4 , December 1984 , pp. 499 - 507
Copyright
Copyright © Cambridge University Press 1984

References

REFERENCES

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