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Register a new userOn the automorphism group of minimal S-adic subshifts of finite alphabet rank
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It has been recently proved that the automorphism group of a minimal subshift with non-superlinear word complexity is virtually $mathbb{Z}$ [DDPM15, CK15]. In this article we extend this result to a broader class proving that the automorphism group of a minimal S-adic subshift of finite alphabet rank is virtually $mathbb{Z}$. The proof is based on a fine combinatorial analysis of the asymptotic classes in this type of subshifts, which we prove are a finite number.
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Dimension groups are complete invariants of strong orbit equivalence for minimal Cantor systems. This paper studies a natural family of minimal Cantor systems having a finitely generated dimension group, namely the primitive unimodular proper S-adic subshifts. They are generated by iterating sequences of substitutions. Proper substitutions are such that the images of letters start with a same letter, and similarly end with a same letter. This family includes various classes of subshifts such as Brun subshifts or dendric subshifts, that in turn include Arnoux-Rauzy subshifts and natural coding of interval exchange transformations. We compute their dimension group and investigate the relation between the triviality of the infinitesimal subgroup and rational independence of letter measures. We also introduce the notion of balanced functions and provide a topological characterization of bal-ancedness for primitive unimodular proper S-adic subshifts.
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