Good potentials for almost isomorphism of countable state Markov shifts

2005/10/28 by Buzzi, Jerome, Mike Boyle, Boyle, Mike M. +1
Computer Science · Mathematics · #37C99 #37D35 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Neural Networks Stability and Synchronization #Primary: 37B10 #Secondary: 37B40

paper · pdf · doi:10.48550/arxiv.math/0510632

openalex publication_date 2005/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Almost isomorphism is an equivalence relation on countable state Markov shifts which provides a strong version of Borel conjugacy; still, for mixing SPR shifts, entropy is a complete invariant of almost isomorphism. In this paper, we establish a class of potentials on countable state Markov shifts whose thermodynamic formalism is respected by almost isomorphism.

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