Geometric Thermodynamical Formalism and Real Analyticity for Meromorphic Functions of Finite Order

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

Working with well chosen Riemannian metrics and employing Nevanlinna's theory, we make the thermodynamical formalism work for a wide class of hyperbolic meromorphic functions of finite order (including in particular exponential family, elliptic functions, cosine, tangent and the cosine--root family and also compositions of these functions with arbitrary polynomials). In particular, the existence of conformal (Gibbs) measures is established and then the existence of probability invariant measures equivalent to conformal measures is proven. As a geometric consequence of the developed thermodynamic formalism, a version of Bowen's formula expressing the Hausdorff dimension of the radial Julia set as the zero of the pressure function and, moreover, the real analyticity of this dimension, is proved.
32 pages

Keywords

Dynamical Systems, 30D05

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/121332

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0606294
 http://arxiv.org/abs/math/0606294

Collections

arXiv