Equilibrium states of interval maps for hyperbolic potentials

2012/10/25 by Huaibin Li, Juan Rivera-Letelier, Li, Huaibin +1 · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1210.6952

We minimized the regularity assumptions on the map. The main results actually apply to maps with flat critical points

arxiv created 2014/04/30 · arxiv updated 2014/05/02

Abstract

We study the thermodynamic formalism of sufficiently regular interval maps for Holder continuous potentials. We show that for a hyperbolic potential there is a unique equilibrium state, and that this measure is exponentially mixing. Moreover, we show the absence of phase transitions: The pressure function is real analytic at such a potential.

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