KMS states for generalized gauge actions on Cuntz-Krieger algebras (An application of the Ruelle-Perron-Frobenius Theorem)

Given a zero-one matrix A we consider certain one-parameter groups of automorphisms of the Cuntz-Krieger algebra O_A, generalizing the usual gauge group, and depending on a positive continuous function H defined on the Markov space \Sigma_A. The main result consists of an application of Ruelle's Perron-Frobenius Theorem to show that these automorphism groups admit a single KMS state.