Thermodynamic formalism of maps satisfying positive expansiveness and specification

Abstract

The relations between equilibrium state, Gibbs state, and eigenvector of the (adjoint) transfer operator are described for maps satisfying positive expansiveness and specification. In particular the author shows how the variational principle defining an equilibrium state can be converted into eigenvalue equations for the transfer operator and its adjoint. The results presented here are largely based on the work of N.T.A. Haydn and the author, relating equilibrium and Gibbs state for homeomorphisms satisfying expansiveness and specification.