Expansive dynamics on zero-dimensional groups

1 June 1987

journal article
research article
Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems

Vol. 7 (2) , 249-261
https://doi.org/10.1017/s0143385700003989

Abstract

If X is a compact, zero-dimensional group and T is an expansive, transitive automorphism then (X, T) is shown to be topologically conjugate to a full shift on finitely many symbols.The problem of classifying such automorphisms up to simultaneous algebraic isomorphism and topological conjugacy is discussed but not solved. It is proved that for any entropy there are only finitely many such equivalence classes. When the entropy is log p for a prime p, there is only one equivalence class. All are then equivalent to

Keywords

This publication has 3 references indexed in Scilit:

Topological entropy and equivalence of dynamical systems
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Classification of Subshifts of Finite Type
Annals of Mathematics, 1973
Lifting expansive homeomorphisms to symbolic flows
Theory of Computing Systems, 1968