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Annales scientifiques de l'ENS - Parutions - série 4, 42 (2009)

Parutions < série 4, 42

ANNALES SCIENTIFIQUES DE L’ÉCOLE NORMALE SUPÉRIEURE, série 4 42, fascicule 4 (2009)

Henk Bruin, Mike Todd
Equilibrium states for interval maps: the potential -t|Df|
Annales scientifiques de l'ENS 42, fascicule 4 (2009), 559-600

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Résumé :
États d'équilibre pour applications de l'intervalle : le potentiel -t |Df|
Soit f:I I 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 _t:x-t|Df(x)| lorsque t est proche de 1, et que la fonction de pression t P(_t) est analytique sur un intervalle approprié près de t=1.

Mots-clefs : États d'équilibre, formalisme thermodynamique, applications de l'intervalle, hyperbolicité non-uniforme

Abstract:
Let f:I 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 _t:x-t|Df(x)| for t close to 1, and also that the pressure function t P(_t) is analytic on an appropriate interval near t = 1.

Keywords: Equilibrium states, thermodynamic formalism, interval maps, non-uniform hyperbolicity

Class. math. : 37D35, 37D25, 37E05


ISSN : 0012-9593
Publié avec le concours de : Centre National de la Recherche Scientifique

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