Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions

TL;DR

This paper explores the application of thermodynamic formalism to transcendental meromorphic and entire functions, focusing on geometric and fractal properties like hyperbolic dimension and pressure functions.

Contribution

It provides a comprehensive overview of thermodynamic formalism in the context of transcendental functions, emphasizing geometric and fractal aspects and their behavior in analytic families.

Findings

Bowen's Formula relates hyperbolic dimension to pressure zero

Analysis of pressure function behavior in function families

Insights into fractal geometry of transcendental functions

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.