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arXiv · 1210.0521

Equilibrium states of weakly hyperbolic one-dimensional maps for Holder potentials

Huaibin Li·Juan Rivera-Letelier
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Abstract

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 Holder continuous potential is hyperbolic. A sample consequence is the absence of phase transitions: The pressure function is real analytic on the space of Holder continuous functions. Another consequence is that every Holder continuous potential has a unique equilibrium state, and that this measure has exponential decay of correlations.

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Huaibin Li, Juan Rivera-Letelier. 2014-03-04. Equilibrium states of weakly hyperbolic one-dimensional maps for Holder potentials. https://arxiv.org/abs/1210.0521

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