Characterization of hyperbolic potentials

For a rational map $f$ and a Hölder continuous potential $ϕ$ satisfying $\supϕ< P(f,ϕ)$ 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 Hölder continuous potentials $ϕ$ for which this property is satisfied for some iterate of $f$.

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