Automorphisms of solenoids and p-adic entropy

Lind, D; Ward, T

doi:10.1017/s0143385700004545

Automorphisms of solenoids and p-adic entropy

Lind, D; Ward, T

Authors

D Lind

T Ward

Abstract

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.

Citation

Lind, D., & Ward, T. (1988). Automorphisms of solenoids and p-adic entropy. Ergodic Theory and Dynamical Systems, 8(3), 411-419. https://doi.org/10.1017/s0143385700004545

Journal Article Type	Article
Publication Date	Sep 1, 1988
Deposit Date	Oct 11, 2012
Publicly Available Date	Nov 8, 2012
Journal	Ergodic Theory and Dynamical Systems
Print ISSN	0143-3857
Electronic ISSN	1469-4417
Publisher	Cambridge University Press
Peer Reviewed	Peer Reviewed
Volume	8
Issue	3
Pages	411-419
DOI	https://doi.org/10.1017/s0143385700004545

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© Copyright Cambridge University Press 1988. This paper has been published by Cambridge University Press in "Ergodic theory and dynamical systems" (8: 3 (1988) 411-419) http://journals.cambridge.org/action/displayJournal?jid=ETS