Characterization of hyperbolic potentials

Published 25 Jun 2010 in math.DS | (1006.5043v2)

Abstract: For a rational map $f$ and a H\"older continuous potential $\phi$ satisfying $$ \sup\phi< P(f,\phi)$$ 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 $\phi$ for which this property is satisfied for some iterate of $f$.

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Authors (1)

Irene Inoquio-Renteria

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