2006/07/21 by Kengo Matsumoto, Matsumoto, Kengo
Computer Science · Mathematics · #37B10 #54H20 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Operator Algebras (math.OA) #math.DS #math.OA #msc:37B10 #msc:54H20 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0607520
40pages, AMStexfile
arxiv created 2006/07/21 · openalex publication_date 2006/07/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notions of symbolic matrix system and λ-graph system for a subshift are generalizations of symbolic matrix and λ-graph (= finite symbolic matrix) for a sofic shift respectively ([Doc. Math. 4(1999), 285-340]). M. Nasu introduced the notion of textile system for a pair of graph homomorphisms to study automorphisms and endomorphisms of topological Markov shifts ([Mem. Amer. Math. Soc. 546,114(1995)]). In this paper, we formulate textile systems on λ-graph systems and study automorphisms on subshifts. We will prove that for a forward automorphism ϕ of a subshift (Λ,σ), the automorphisms ϕk σn, k≥ 0, n≥ 1 can be explicitly realized as a subshift defined by certain symbolic matrix systems coming from both the strong shift equivalence representing ϕ and the subshift (Λ,σ). As an application of this result, if an automorphism ϕ of a subshift Λ is a simple automorphism, the dynamical system (Λ, ϕ∘ σ) is topologically conjugate to the subshift (Λ, σ).