A characterization of hyperbolic potentials of rational maps

Autor(es)

Inoquio-Renteria, Irene ^[1] ; Rivera-Letelier, Juan ^[2]

Afiliação do(s) autor(es)

^[1] ICMC USP Sao Carlos, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil

^[2] Pontificia Univ Catolica Chile, Fac Matemat, Santiago - Chile

• Tipo de documento: Artigo Científico
• Fonte: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 43, n. 1, p. 99-127, MAR 2012.
• Citações Web of Science: 15

Resumo

Consider a rational map f of degree at least 2 acting on its Julia set J(f), a Holder continuous potential phi : J(f) -> R and the pressure P(f, phi). In the case where sup phi < P(f, phi), J(f) the uniqueness and stochastic properties of the corresponding equilibrium states have been extensively studied. In this paper we characterize those potentials phi for which this property is satisfied for some iterate off, in terms of the expanding properties of the corresponding equilibrium states. A direct consequence of this result is that for a non-uniformly hyperbolic rational map every Holder continuous potential has a unique equilibrium state and that this measure is exponentially mixing. (AU)

• Processo FAPESP: 10/07267-4 - Teoria da renormalização e formalismo termodinâmico
• Beneficiário: Irene Raquel Inoquio Renteria
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado