Characterization of hyperbolic potentials

Abstract

For a rational map $f$ and a Hölder 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 Hölder continuous potentials $\varphi$ for which this property is satisfied for some iterate of $f$.

This paper has been withdrawn due to upload of another version of it as a new preprint

References in corpus (1)

• Nice inducing schemes and the thermodynamics of rational maps