Let be a multimodal interval map satisfying polynomial growth of the derivatives along critical orbits. We prove the existence and uniqueness of equilibrium states for the potential for close to , and also that the pressure function is analytic on an appropriate interval near .
Soit une application multimodale de classe dont les dérivées le long des orbites des points critiques sont à croissance polynomiale, où est un intervalle. Nous démontrons l’existence et l’unicité d’un état d’équilibre pour le potentiel lorsque est proche de , et que la fonction de pression est analytique sur un intervalle approprié près de .
Keywords: equilibrium states, thermodynamic formalism, interval maps, non-uniform hyperbolicity
Mot clés : États d'équilibre, formalisme thermodynamique, applications de l'intervalle, hyperbolicité non-uniforme
@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}, pages = {559--600}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {Ser. 4, 42}, number = {4}, year = {2009}, doi = {10.24033/asens.2103}, mrnumber = {2568876}, zbl = {1192.37051}, language = {en}, url = {http://www.numdam.org/articles/10.24033/asens.2103/} }
TY - JOUR AU - Bruin, Henk AU - Todd, Mike TI - Equilibrium states for interval maps: the potential $-t\log |Df|$ JO - Annales scientifiques de l'École Normale Supérieure PY - 2009 SP - 559 EP - 600 VL - 42 IS - 4 PB - Société mathématique de France UR - http://www.numdam.org/articles/10.24033/asens.2103/ DO - 10.24033/asens.2103 LA - en ID - ASENS_2009_4_42_4_559_0 ER -
%0 Journal Article %A Bruin, Henk %A Todd, Mike %T Equilibrium states for interval maps: the potential $-t\log |Df|$ %J Annales scientifiques de l'École Normale Supérieure %D 2009 %P 559-600 %V 42 %N 4 %I Société mathématique de France %U http://www.numdam.org/articles/10.24033/asens.2103/ %R 10.24033/asens.2103 %G en %F 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/articles/10.24033/asens.2103/
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