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 language | English (US) |
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Article number | e5 |
Journal | Forum of Mathematics, Sigma |
Volume | 3 |
DOIs | |
State | Published - 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