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Automorphisms of solenoids and p-adic entropy*

Published online by Cambridge University Press:  19 September 2008

D. A. Lind  and
T. Ward
D. A. Lind
Affiliation:
Department of Mathematics, University of Washington, Seattle, WA 98195, USA
T. Ward
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, England
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Abstract

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We show that a full solenoid is locally the product of a euclidean component and p-adic components for each rational prime p. An automorphism of a solenoid preserves these components, and its topological entropy is shown to be the sum of the euclidean and p-adic contributions. The p-adic entropy of the corresponding rational matrix is computed using its p-adic eigenvalues, and this is used to recover Yuzvinskii's calculation of entropy for solenoidal automorphisms. The proofs apply Bowen's investigation of entropy for uniformly continuous transformations to linear maps over the adele ring of the rationals.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Issue 3 , September 1988 , pp. 411 - 419
Copyright
Copyright © Cambridge University Press 1988

References

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