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arXiv · 0704.2199

Equilibrium states for interval maps: the potential $-t\log |Df|$

Henk Bruin·Mike Todd
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Abstract

Let $f:I \to I$ be a $C^2$ multimodal interval map satisfying polynomial growth of the derivatives along critical orbits. We prove the existence and uniqueness of equilibrium states for the potential $ϕ_t:x\mapsto -t\log|Df(x)|$ for $t$ close to 1, and also that the pressure function $t \mapsto P(ϕ_t)$ is analytic on an appropriate interval near $t = 1$.

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Henk Bruin, Mike Todd. 2008-02-19. Equilibrium states for interval maps: the potential $-t\log |Df|$. https://arxiv.org/abs/0704.2199

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