TITLE:
A Class of Potentials for Hyperbolic Transcendental Entire Maps
AUTHORS:
Irene Inoquio-Renteria
KEYWORDS:
Thermodynamic Formalism, Entire Transcendental Functions, Tame Potentials
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.13 No.8,
August
11,
2023
ABSTRACT: We identify a class of transcendental entire maps of finite order, of disjoint-type, satisfying the rapid derivative growth condition. Within this class, we show that there exist hyperbolic transcendental entire maps that generate a large class of potentials which intersect the so-called tame potentials and form a distinct class of potentials. The methods and techniques derived from the thermodynamic formalism are applied to these potentials for transcendental entire maps acting on some subset of the Julia set which is conjugated to the shift map over a code space with a countable alphabet endowed with the euclidean induced metric on the complex plane.