Characterization of hyperbolic potentials

Details Characterization of hyperbolic potentials Characterization of hyperbolic potentials

2010-06-25

arxiv.org/abs/1006.5043v2

Mathematics

Dynamical Systems

This paper has been withdrawn due to upload of another version of it as a new preprint

Scientific paper

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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