Ergodic Theory and Dynamical Systems

Existence, uniqueness and ratio decomposition for Gibbs states via duality

A. A. PINTO a1 and D. A. RAND a2
a1 Departamento de Matemática Aplicada, Faculdade de Ciências, Universidade do Porto, 4000 Porto, Portugal (e-mail:
a2 Nonlinear Systems Laboratory, Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK (e-mail:


We give an elementary proof of existence and uniqueness of Gibbs states for Hölder weight systems on subshifts of finite type. This uses a notion of duality for such subshifts. The approach of Paterson [2] is used to construct a measure with a prescribed Jacobian and the duality is used to produce an invariant measure from this

(Received November 20 1998)
(Revised April 4 2000)