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- W4298045502 abstract "For a finite alphabet $mathcal{A}$ and shift $Xsubseteqmathcal{A}^{mathbb{Z}}$ whose factor complexity function grows at most linearly, we study the algebraic properties of the automorphism group ${rm Aut}(X)$. For such systems, we show that every finitely generated subgroup of ${rm Aut}(X)$ is virtually ${mathbb Z}^d$, in contrast to the behavior when the complexity function grows more quickly. With additional dynamical assumptions we show more: if $X$ is transitive, then ${rm Aut}(X)$ is virtually $mathbb Z$; if $X$ has dense aperiodic points, then ${rm Aut}(X)$ is virtually ${mathbb Z}^d$. We also classify all finite groups that arise as the automorphism group of a shift." @default.
- W4298045502 created "2022-10-01" @default.
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- W4298045502 date "2014-11-01" @default.
- W4298045502 modified "2023-10-13" @default.
- W4298045502 title "The automorphism group of a shift of linear growth: beyond transitivity" @default.
- W4298045502 doi "https://doi.org/10.48550/arxiv.1411.0180" @default.
- W4298045502 hasPublicationYear "2014" @default.
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