Abstract
Consider a rational map f of degree at least 2 acting on its Julia set J(f), a Hölder continuous potential φ: J(f) → ℝ and the pressure P(f,φ). In the case where
the uniqueness and stochastic properties of the corresponding equilibrium states have been extensively studied. In this paper we characterize those potentials φ for which this property is satisfied for some iterate of f, in terms of the expanding properties of the corresponding equilibrium states. A direct consequence of this result is that for a non-uniformly hyperbolic rational map every Hölder continuous potential has a unique equilibrium state and that this measure is exponentially mixing.
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Partially supported by FAPESP 2010/07267-4.
Partially supported by FONDECYT N 1100922.
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Inoquio-Renteria, I., Rivera-Letelier, J. A characterization of hyperbolic potentials of rational maps. Bull Braz Math Soc, New Series 43, 99–127 (2012). https://doi.org/10.1007/s00574-012-0007-1
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DOI: https://doi.org/10.1007/s00574-012-0007-1