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EXPANSIVENESS, ENTROPY AND POLYNOMIAL-GROWTH FOR GROUPS ACTING ON SUBSHIFTS BY AUTOMORPHISMS
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UNSPECIFIED (1993) EXPANSIVENESS, ENTROPY AND POLYNOMIAL-GROWTH FOR GROUPS ACTING ON SUBSHIFTS BY AUTOMORPHISMS. INDAGATIONES MATHEMATICAE-NEW SERIES, 4 (2). pp. 203-210. ISSN 0019-3577.
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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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | INDAGATIONES MATHEMATICAE-NEW SERIES | ||||
Publisher: | ELSEVIER SCIENCE BV | ||||
ISSN: | 0019-3577 | ||||
Official Date: | 21 June 1993 | ||||
Dates: |
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Volume: | 4 | ||||
Number: | 2 | ||||
Number of Pages: | 8 | ||||
Page Range: | pp. 203-210 | ||||
Publication Status: | Published |
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