Natural Equilibrium States for Multimodal Maps |
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Authors: | Godofredo Iommi Mike Todd |
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Institution: | 1. Facultad de Matemáticas, Pontificia Universidad Católica de Chile (PUC), Avenida Vicu?a Mackenna, 4860, Santiago, Chile 2. Departamento de Matemática Pura, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre, 687, 4169-007, Porto, Portugal 3. Department of Mathematics and Statistics, Boston University, 111 Cummington Street, Boston, MA, 2215, USA
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Abstract: | This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains,
but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium states for
the geometric potentials −t log |Df|, for the largest possible interval of parameters t. We also study the regularity and convexity properties of the pressure function, completely characterising the first order
phase transitions. Results concerning the existence of absolutely continuous invariant measures with respect to the Lebesgue
measure are also obtained. |
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Keywords: | |
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