Equilibrium states for interval maps: the potential -tlog|Df|
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 42 (2009) no. 4, p. 559-600

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.

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.

DOI : https://doi.org/10.24033/asens.2103
Classification:  37D35,  37D25,  37E05
Keywords: equilibrium states, thermodynamic formalism, interval maps, non-uniform hyperbolicity
@article{ASENS_2009_4_42_4_559_0,
     author = {Bruin, Henk and Todd, Mike},
     title = {Equilibrium states for interval maps: the potential $-t\log |Df|$},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 42},
     number = {4},
     year = {2009},
     pages = {559-600},
     doi = {10.24033/asens.2103},
     zbl = {1192.37051},
     mrnumber = {2568876},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2009_4_42_4_559_0}
}
Bruin, Henk; Todd, Mike. Equilibrium states for interval maps: the potential $-t\log |Df|$. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 42 (2009) no. 4, pp. 559-600. doi : 10.24033/asens.2103. http://www.numdam.org/item/ASENS_2009_4_42_4_559_0/

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