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

Abstract

In the context of smooth interval maps, we study an inducing scheme approach to prove existence and uniqueness of equilibrium states for potentials $\varphi$ with he `bounded range' condition $\sup ϕ- \inf ϕ< \htop$, 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 Hölder continuous. We also prove analyticity of the pressure in this context.

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