Gibbs states and equilibrium states for finitely presented dynamical systems (Q1182241)

The equivalence between equilibrium states and translation-invariant Gibbs states for lattice spin systems is a central theorem of statistical mechanics. The result has been translated with a help of symbolic dynamics, to the field of hyperbolic dynamical systems, more precisely, Axiom A diffeomorphisms. In this paper the author generalizes the equivalence to finitely presented systems, a wider class of dynamical systems recently introduced by Fried. This class contains pseudo-Anosov homeomorphisms and sofic shifts and is a naturalization of Axiom A. In fact the systems possess very good symbolic dynamics and the methods from the thermodynamic formalism which apply to Axiom A diffeomorphisms carry over to this case.