2023/07/03 by Nasser Golestani, Golestani, Nasser, Maryam Hosseini +3
Computer Science · Mathematics · #19K14 #37B05 #37B10 #54H20 #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2307.01156
openalex publication_date 2023/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that every topological factoring between two zero dimensional dynamical systems can be represented by a sequence of morphisms between the levels of the associated ordered Bratteli diagrams. Conversely, we will prove that given an ordered Bratteli diagram B with a continuous Vershik map on it, every sequence of morphisms between levels of B and C, where C is another ordered Bratteli diagram with continuous Vershik map, induces a topological factoring if and only if B has a unique infinite min path. We present a method to construct various examples of ordered premorphisms between two decisive Bratteli diagrams such that the induced maps between the two Vershik systems are not topological factorings. We provide sufficient conditions for the existence of a topological factoring from an ordered premorphism. Expanding on the modelling of factoring, we generalize the Curtis-Hedlund-Lyndon theorem to represent factor maps between two zero dimensional dynamical systems through sequences of sliding block codes.