THE AUTOMORPHISM GROUP OF A SHIFT OF LINEAR GROWTH: BEYOND TRANSITIVITY

Van Cyr, Bryna Kra

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

For a finite alphabet A and shift X ⊆ AZ whose factor complexity function grows at most linearly, we study the algebraic properties of the automorphism group Aut(X). For such systems, we show that every finitely generated subgroup of Aut(X) is virtually ℤd, in contrast to the behavior when the complexity function grows more quickly. With additional dynamical assumptions we show more: if X is transitive, then Aut(X) is virtually ℤ; if X has dense aperiodic points, then Aut(X) is virtually ℤd. We also classify all finite groups that arise as the automorphism group of a shift.

Original languageEnglish (US)
Article numbere5
JournalForum of Mathematics, Sigma
Volume3
DOIs
StatePublished - Jan 1 2015

ASJC Scopus subject areas

  • Analysis
  • Theoretical Computer Science
  • Algebra and Number Theory
  • Statistics and Probability
  • Mathematical Physics
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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