Expansive dynamics on zero-dimensional groups

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 [omitted formula]. © 1987, Foundation for Environmental Conservation. All rights reserved.