Equilibrium states for potentials with $\supφ- \infφ< \htop(f)$

Details Equilibrium states for potentials with $\supφ- \infφ< \htop(f)$ Equilibrium states for potentials with $\supφ- \infφ< \htop(f)$

2007-08-02

arxiv.org/abs/0708.0374v2

Commun. Math. Phys. 283 (2008) 579-611

Mathematics

Dynamical Systems

Added Lemma 6 to deal with the disparity between leading eigenvalues and operator norms. Added extra references and corrected

Scientific paper

10.1007/s00220-008-0596-0

In the context of smooth interval maps, we study an inducing scheme approach to prove existence and uniqueness of equilibrium states for potentials $\phi$ with he `bounded range' condition $\sup \phi - \inf \phi < \htop$, first used by Hofbauer and Keller. We compare our results to Hofbauer and Keller's use of Perron-Frobenius operators. We demonstrate that this `bounded range' condition on the potential is important even if the potential is H\"older continuous. We also prove analyticity of the pressure in this context.

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