zbMATH — the first resource for mathematics

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 \(t=1\).

37E05 Dynamical systems involving maps of the interval
37D35 Thermodynamic formalism, variational principles, equilibrium states for dynamical systems
PDF BibTeX Cite
Full Text: DOI Link arXiv