Thermodynamic Formalism for a Class of Hyperbolic Transcendental Meromorphic Functions

2025/06/07 by Hamid Naderiyan, Naderiyan, Hamid
Mathematics · #30 #37 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2506.06760

openalex publication_date 2025/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Thermodynamical Formalism and Multifractal Analysis for Meromorphic Functions of finite order

Related

• Geometric Thermodynamical Formalism and Real Analyticity for Meromorphic Functions of Finite Order
• Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions
• Random Dynamics of Transcendental Functions
• Thermodynamical Formalism and Multifractal Analysis for Meromorphic Functions of finite order
• Thermodynamic formalism for entire transcendental maps with hyperbolic Baker Domains