On a class of one-sided Markov shifts

2004/06/03 by Ben-Zion Rubshtein, Rubshtein, Ben-Zion
Computer Science · Mathematics · #37A35 (Primary) #60J10 (Secondary) #Advanced Topology and Set Theory #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #math.DS #math.PR #msc:37A35 #msc:60J10

paper · pdf · doi:10.48550/arxiv.math/0406059

arxiv created 2004/06/03 · openalex publication_date 2004/06/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study one-sided Markov shifts, corresponding to positively recurrent Markov chains with countable (finite or infinite) state spaces. The following classification problem is considered: when two one-sided Markov shifts are isomorphic up to a measure preserving isomorphism In this paper we solve the problem for the class of rho-uniform (or finitely rho-Bernoulli) one-sided Markov shifts considered in Ru₆ We show that every ergodic rho-uniform Markov shift T can be represented in a canonical form T = T_G by means of a canonical (uniquely determined by T) stochastic graph G. In the canonical form, two such shifts T_G1 and T_G2 are isomorphic if and only if their canonical stochastic graphs G₁ and G₂ are isomorphic.

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