| Full text | |
| Author(s): |
Total Authors: 2
|
| Affiliation: | [1] ICMC USP Sao Carlos, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil
[2] Pontificia Univ Catolica Chile, Fac Matemat, Santiago - Chile
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 43, n. 1, p. 99-127, MAR 2012. |
| Web of Science Citations: | 15 |
| Abstract | |
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) | |
| FAPESP's process: | 10/07267-4 - Remormalization theory and thermodynamic formalism |
| Grantee: | Irene Raquel Inoquio Renteria |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |