Characterization of hyperbolic potentials

For a rational map $f$ and a H"older continuous potential $\varphi$ satisfying $$\sup \varphi <P(f,\varphi )$$ the uniqueness and stochastic properties of the corresponding equilibrium states have been extensively studied. For a given rational map $f$, in this paper we characterize those H"older continuous potentials $\varphi$ for which this property is satisfied for some iterate of $f$.