# Equilibrium States of Weakly Hyperbolic One-Dimensional Maps for Hölder Potentials

@article{Li2012EquilibriumSO,
title={Equilibrium States of Weakly Hyperbolic One-Dimensional Maps for H{\"o}lder Potentials},
author={Huaibin Li and Juan Rivera-Letelier},
journal={Communications in Mathematical Physics},
year={2012},
volume={328},
pages={397-419}
}
• Published 1 October 2012
• Mathematics
• Communications in Mathematical Physics
There is a wealth of results in the literature on the thermodynamic formalism for potentials that are, in some sense, “hyperbolic”. We show that for a sufficiently regular one-dimensional map satisfying a weak hyperbolicity assumption, every Hölder continuous potential is hyperbolic. A sample consequence is the absence of phase transitions: The pressure function is real analytic on the space of Hölder continuous functions. Another consequence is that every Hölder continuous potential has a…
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