Thermodynamic Formalism for a Class of Hyperbolic Transcendental Meromorphic Functions
Dynamical Systems
2025-06-10 v1 Complex Variables
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.
Keywords
Cite
@article{arxiv.2506.06760,
title = {Thermodynamic Formalism for a Class of Hyperbolic Transcendental Meromorphic Functions},
author = {Hamid Naderiyan},
journal= {arXiv preprint arXiv:2506.06760},
year = {2025}
}