Bruin, Henk; Todd, Mike
Equilibrium states for interval maps: the potential -tlog|Df|  [ États d’équilibre pour applications de l’intervalle : le potentiel -tlog|Df| ]
Annales scientifiques de l'École Normale Supérieure, Série 4 : Tome 42 (2009) no. 4 , p. 559-600
Zbl 1192.37051 | MR 2568876 | 1 citation dans Numdam
doi : 10.24033/asens.2103
URL stable : http://www.numdam.org/item?id=ASENS_2009_4_42_4_559_0

Classification:  37D35,  37D25,  37E05
Mots clés: États d'équilibre, formalisme thermodynamique, applications de l'intervalle, hyperbolicité non-uniforme
Soit f:II une application multimodale de classe C 2 dont les dérivées le long des orbites des points critiques sont à croissance polynomiale, où I est un intervalle. Nous démontrons l’existence et l’unicité d’un état d’équilibre pour le potentiel φ t :x-tlog|Df(x)| lorsque t est proche de 1, et que la fonction de pression tP(φ t ) est analytique sur un intervalle approprié près de t=1.
Let f:II 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 φ t :x-tlog|Df(x)| for t close to 1, and also that the pressure function tP(φ t ) is analytic on an appropriate interval near t=1.

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