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

  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},
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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