Automorphisms of solenoids and p-adic entropy

Lind, D; Ward, T

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
• Public URL: https://durham-repository.worktribe.com/output/1472389