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Some results on the classification of expansive automorphisms of compact abelian groups

Published online by Cambridge University Press:  19 September 2008

Fabio Fagnani
Fabio Fagnani
Affiliation:
Scuola Normale Superiore, Piazza dei Cavalieri 7, 56100 Pisa, Italy
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Abstract

In this paper we study expansive automorphisms of compact 0-dimensional abelian groups. Our main result is the complete algebraic and topological classification of the transitive expansive automorpisms for which the maximal order of the elements is p2 for a prime p. This yields a classification of the transitive expansive automorphisms with topological entropy log p2. Finally, we prove a necessary and sufficient condition for an expansive automorphism to be conjugated, topologically and algebraically, to a shift over a finite group.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 1 , February 1996 , pp. 45 - 50
Copyright
Copyright © Cambridge University Press 1996

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References

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