The Library
EXPANSIVENESS, ENTROPY AND POLYNOMIAL-GROWTH FOR GROUPS ACTING ON SUBSHIFTS BY AUTOMORPHISMS
Tools
Tools
Tools
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
Full text not available from this repository.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 |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Journal or Publication Title: | INDAGATIONES MATHEMATICAE-NEW SERIES |
| Publisher: | ELSEVIER SCIENCE BV |
| ISSN: | 0019-3577 |
| Date: | 21 June 1993 |
| Volume: | 4 |
| Number: | 2 |
| Number of Pages: | 8 |
| Page Range: | pp. 203-210 |
| Publication Status: | Published |
| URI: | http://wrap.warwick.ac.uk/id/eprint/21226 |
Data sourced from Thomson Reuters' Web of Knowledge
Actions (login required)
 |
View Item |
