Good potentials for almost isomorphisms of countable state Markov shifts

Mike Boyle, Jérôme Buzzi and Ricardo Gómez

Stochastics and Dynamics 7 Vol. 1 (2007) 1-15.

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 [BBG]. 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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