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    Zhao, Yun Cao, Yongluo and Wang, Juan 2014. Dimension estimates in non-conformal setting. Discrete and Continuous Dynamical Systems, Vol. 34, Issue. 9, p. 3847.


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Geometric thermodynamic formalism and real analyticity for meromorphic functions of finite order

  • VOLKER MAYER (a1) and MARIUSZ URBAŃSKI (a2)
  • DOI: http://dx.doi.org/10.1017/S0143385707000648
  • Published online: 01 June 2008
Abstract
Abstract

Working with well chosen Riemannian metrics and employing Nevanlinna’s theory, we make the thermodynamic 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.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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