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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.

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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