Equilibrium states of weakly hyperbolic one-dimensional maps for Holder potentials
Dynamical Systems
2014-03-05 v3
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.
Keywords
Cite
@article{arxiv.1210.0521,
title = {Equilibrium states of weakly hyperbolic one-dimensional maps for Holder potentials},
author = {Huaibin Li and Juan Rivera-Letelier},
journal= {arXiv preprint arXiv:1210.0521},
year = {2014}
}
Comments
Minor corrections. arXiv admin note: text overlap with arXiv:1307.1297