# American Institute of Mathematical Sciences

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May  2015, 35(5): 2273-2298. doi: 10.3934/dcds.2015.35.2273

## Dynamics of hyperbolic meromorphic functions

 1 Department of Mathematical Sciences, Tsinghua University, Beijing, China

Received  October 2010 Revised  June 2014 Published  December 2014

A definition of hyperbolic meromorphic functions is given and then we discuss the dynamical behavior and the thermodynamic formalism of hyperbolic functions on their Julia sets. We prove the important expanding properties for hyperbolic functions on the complex plane or with respect to the Euclidean metric. We establish the Bowen formula for hyperbolic functions on the complex plane, that is, the Poincare exponent equals to the Hausdorff dimension of the radial Julia set and furthermore, we prove that all the results in the Walters' theory hold for hyperbolic functions on the Riemann sphere.
Citation: Jian-Hua Zheng. Dynamics of hyperbolic meromorphic functions. Discrete & Continuous Dynamical Systems - A, 2015, 35 (5) : 2273-2298. doi: 10.3934/dcds.2015.35.2273
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