EXPANSIVENESS, ENTROPY AND POLYNOMIAL-GROWTH FOR GROUPS ACTING ON SUBSHIFTS BY AUTOMORPHISMS
UNSPECIFIED. (1993) EXPANSIVENESS, ENTROPY AND POLYNOMIAL-GROWTH FOR GROUPS ACTING ON SUBSHIFTS BY AUTOMORPHISMS. INDAGATIONES MATHEMATICAE-NEW SERIES, 4 (2). pp. 203-210. ISSN 0019-3577Full text not available from this repository.
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|
|Subjects:||Q Science > QA Mathematics|
|Journal or Publication Title:||INDAGATIONES MATHEMATICAE-NEW SERIES|
|Publisher:||ELSEVIER SCIENCE BV|
|Official Date:||21 June 1993|
|Number of Pages:||8|
|Page Range:||pp. 203-210|
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