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Thermodynamical Formalism and Multifractal Analysis for Meromorphic Functions of finite order

Volker Mayer·Mariusz Urbanski
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Abstract

We first use Nevanlinna theory to provide full thermodynamical formalism for a very general class of meromorphic functions of finite order. Finer stochastic properties of the Perron-Frobenius operator are given and finally we provide the multifractal analysis of Gibbs states.

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Volker Mayer, Mariusz Urbanski. 2009-01-31. Thermodynamical Formalism and Multifractal Analysis for Meromorphic Functions of finite order. https://arxiv.org/abs/math/0701275

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