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Equilibrium states for interval maps: the potential $$-t \log |Df|$$. (English) Zbl 1192.37051
Let $$f: I\to I$$ be a $$C^2$$ multimodal interval map satisfying polynomial growth of the derivatives along critical orbits. The paper establishes the existence and uniqueness of equilibrium states for the potential $$\varphi_t:x\to -t\log |Df(x)|$$ for $$t$$ close to 1. It is also shown that the pressure function $$t\to P(\varphi(t))$$ is analytic on an appropriate interval near $$t=1$$.

##### MSC:
 37E05 Dynamical systems involving maps of the interval 37D35 Thermodynamic formalism, variational principles, equilibrium states for dynamical systems
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