Almost isomorphism for countable state Markov shifts

2004/05/09 by Mike M. Boyle, Jérôme Buzzi, Jerome Buzzi +5
Computer Science · Mathematics · #37B10 #37B40 #37C99 #37D35 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS #msc:37B10 #msc:37B40 #msc:37C99 #msc:37D35

paper · pdf · doi:10.48550/arxiv.math/0405154

arxiv created 2004/05/09 · openalex publication_date 2004/05/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Countable state Markov shifts are a natural generalization of the well-known subshifts of finite type. They are the subject of current research both for their own sake and as models for smooth dynamical systems. In this paper, we investigate their almost isomorphism and entropy conjugacy and obtain a complete classification for the especially important class of strongly positive recurrent Markov shifts. This gives a complete classification up to entropy conjugacy of the natural extensions of smooth entropy expanding maps, including all smooth interval maps with non-zero topological entropy.

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