2023/07/04 by Álvaro Bustos-Gajardo, Bustos-Gajardo, Alvaro, Johannes Kellendonk +3
Biochemistry, Genetics and Molecular Biology · Computer Science · #20M10 #20M35 #37B02 #37B10 #37B52 #Chemical Synthesis and Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2307.01787
openalex publication_date 2023/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.