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arXiv · 0708.0374

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

Henk Bruin·Mike Todd
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Abstract

In the context of smooth interval maps, we study an inducing scheme approach to prove existence and uniqueness of equilibrium states for potentials $ϕ$ 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.

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Henk Bruin, Mike Todd. 2008-08-14. Equilibrium states for potentials with $\supϕ- \infϕ< \htop(f)$. https://doi.org/10.1007/s00220-008-0596-0

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