Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions

2020/07/31 by Mayer, Volker, Urbanski, Mariusz
#30D05 #37F10 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.15875

Abstract

This text provides an overview of the (geometric) thermodynamic formalism for transcendental meromorphic and entire functions with particular emphasis on geometric/fractal aspects such as Bowen's Formula expressing the hyperbolic dimension as a unique zero of a pressure function and the behavior of the latter when the transcendental functions vary in an analytic family.

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