For hyperbolic transcendental meromorphic functions of the Bergweiler-Kotus class, the paper proves existence and uniqueness of the conformal measure and the invariant Gibbs measure for the geometric potential.
Meromorphic dynamics
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Thermodynamic Formalism for a Class of Hyperbolic Transcendental Meromorphic Functions
For hyperbolic transcendental meromorphic functions of the Bergweiler-Kotus class, the paper proves existence and uniqueness of the conformal measure and the invariant Gibbs measure for the geometric potential.