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EXPANSIVENESS, ENTROPY AND POLYNOMIAL-GROWTH FOR GROUPS ACTING ON SUBSHIFTS BY AUTOMORPHISMS

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Abstract

Let X be a closed translationally invariant subset of the d-dimensional full shift P(Zd), where P is a finite set, and suppose that the Z(d)-action on X by translations has positive topological entropy. Let G be a finitely generated group of polynomial growth. We prove that if growth(G)<d, then any G-action on X by homeomorphisms commuting with translations is not expansive. On the other hand, if growth(G) = d, then any expansive G-action on X by homeomorphisms commuting with translations has positive topological entropy. Analogous results hold for semigroups

Topics: QA
Publisher: ELSEVIER SCIENCE BV
OAI identifier: oai:wrap.warwick.ac.uk:21226
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