Journal Articles Monatshefte für Mathematik Year : 2025

Almost automorphic and bijective factors of substitution shifts

Abstract

In this article we completely characterise constant length substitution shifts which have a proper almost automorphic factor, or which have a bijective substitution factor such that the factor map is injective on at least one point. Our approach is algebraic: we characterise these dynamical properties in terms of a finite semigroup defined by the substitution. We characterise the existence of almost automorphic factors in terms of Green's R-relation and the existence of bijective factors in terms of Green's L-relation. Our results are constructive.

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Dates and versions

hal-04831424 , version 1 (17-02-2025)

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Alvaro Bustos-Gajardo, Johannes Kellendonk, Reem Yassawi. Almost automorphic and bijective factors of substitution shifts. Monatshefte für Mathematik, 2025, ⟨10.1007/s00605-024-02053-y⟩. ⟨hal-04831424⟩
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