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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