Thermodynamic Formalism for a Class of Hyperbolic Transcendental Meromorphic Functions

TL;DR

This paper develops a thermodynamic formalism framework for a specific class of hyperbolic transcendental meromorphic functions, proving the existence and uniqueness of key measures in complex dynamics.

Contribution

It establishes the thermodynamic formalism for B-class hyperbolic transcendental meromorphic functions, including existence and uniqueness of conformal and Gibbs measures.

Findings

Existence of conformal measure

Uniqueness of invariant Gibbs measure

Framework applicable to B-class functions

Abstract

This paper studies the thermodynamic formalism in the context of complex dynamics. We establish the thermodynamics formalism for the class of hyperbolic transcendental meromorphic functions of B-class, where the poles have bounded multiplicities, the Nevanlinna order is finite, and infinity is not an asymptotic value. We showed the existence and uniqueness of the conformal measure and the invariant Gibbs measure equivalent to the conformal measure.