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

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

References in corpus (2)

• Almost Sure Invariance Principle For Nonuniformly Hyperbolic Systems
• Markov extensions and lifting measures for complex polynomials

Cited by in corpus (4)

• Statistical stability of equilibrium states for interval maps
• Nice inducing schemes and the thermodynamics of rational maps
• Return time statistics for invariant measures for interval maps with positive Lyapunov exponent
• Invariant measures of minimal post-critical sets of logistic maps