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

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

2007-04-17

arxiv.org/abs/0704.2199v4

Ann. Sci. Ecole Norm. Sup. (4) 42 (2009) 559-600.

Mathematics

Dynamical Systems

Scientific paper

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 $\phi_t:x\mapsto
-t\log|Df(x)|$ for $t$ close to 1, and also that the pressure function $t
\mapsto P(\phi_t)$ is analytic on an appropriate interval near $t = 1$.

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