On the automorphism groups of multidimensional shifts of finite type

Michael Hochman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

We investigate algebraic properties of the automorphism group of multidimensional shifts of finite type (SFTs). We show that positive entropy implies that the automorphism group contains every finite group and, together with transitivity, implies that the center of the automorphism group is trivial (i.e.consists only of the shift action). We also show that positive entropy and dense minimal points (in particular, dense periodic points) imply that the automorphism group of X contains a copy of the automorphism group of the one-dimensional full shift, and hence contains non-trivial elements of infinite order. On the other hand we construct a mixing, positive-entropy SFT whose automorphism group is, modulo the shift action, a union of finite groups.

Original languageAmerican English
Pages (from-to)809-840
Number of pages32
JournalErgodic Theory and Dynamical Systems
Volume30
Issue number3
DOIs
StatePublished - Jun 2010
Externally publishedYes

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