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arXiv · 2307.01787

Almost automorphic and bijective factors of substitution shifts

Alvaro Bustos-Gajardo·Johannes Kellendonk·Reem Yassawi
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Abstract

In this article we completely characterise constant length substitution shifts which have an almost automorphic factor, or which have a bijective substitution factor. Our approach is algebraic: we study 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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Alvaro Bustos-Gajardo, Johannes Kellendonk, Reem Yassawi. 2023-07-04. Almost automorphic and bijective factors of substitution shifts. https://arxiv.org/abs/2307.01787

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