Automorphisms of solenoids and p-adic entropy

Lind, D. A. and Ward, T. (1988) Automorphisms of solenoids and p-adic entropy. Ergodic Theory and Dynamical Systems, 8 (03). pp. 411-419. ISSN 0143-3857

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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.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:48
Last Modified: 24 Oct 2022 04:17
DOI: 10.1017/S0143385700004545


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