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Automorphisms of solenoids and p-adic entropy.

Lind, D. and Ward, T. (1988) 'Automorphisms of solenoids and p-adic entropy.', Ergodic theory and dynamical systems., 8 (3). pp. 411-419.


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.

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Publisher statement:© 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)
Record Created:11 Oct 2012 15:20
Last Modified:08 Nov 2012 11:20

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