On Conjugacy Invariants of D_∞-Topological Markov Chains

2014/07/15 by Sieye Ryu, Ryu, Sieye
Computer Science · Mathematics · #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Graph theory and applications #Topological and Geometric Data Analysis #math.DS

paper · pdf · doi:10.48550/arxiv.1407.3988

openalex publication_date 2014/07/15 · arxiv created 2017/12/10 · arxiv updated 2017/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A D_∞-topological Markov chain can be represented by a pair of zero-one square matrices, which is called a flip pair. We introduce the concepts of D_∞-strong shift equivalence and D_∞-shift equivalence, which are equivalence relations between flip pairs. We investigate the relationships between the existence of a D_∞-conjugacy, the existence of a D_∞-strong shift equivalence, the existence of a D_∞-shift equivalence and the coincidence of the Lind zeta functions.

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