Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions

In this survey we deal with transcendental meromorphic and entire functions. We thoroughly discuss in context close relations between topological pressure conformal measures for geometric potentials. For two more special classes of functions, namely dynamically semi-regular those the class \(\mathcal {D}\) that have negative spectrum, then also discuss, by means appropriate transfer (or Perron-Frobenius) operator, corresponding thermodynamic formalism such It holds its full classical version. At end hyperbolic dimension, Bowen’s Formula, real analyticity Hausdorff dimension.