Examples for the nonuniqueness of the equilibrium state

Abstract

In this paper equilibrium states on shift spaces are considered. A uniqueness theorem for equilibrium states is proved. Then we study a particular class of continuous functions. We characterize the functions of this class which satisfy Ruelle’s Perron-Frobenius condition, those which admit a measure determined by a homogeneity condition, and those which have unique equilibrium state. In particular, we get examples for the nonuniqueness of the equilibrium state.