Thermodynamic formalism for entire transcendental maps with hyperbolic Baker Domains

We provide a version of a thermodynamic formalism of entire transcendental maps that exhibit Baker domains, denoted as \(f_{\ell, c}: \mathbb C\to \mathbb C\) and defined by \(f_{\ell, c}(z)= c-(\ell-1)\log c+ \ell z- e^z\), where \(\ell \in \mathbb N\), with \(\ell \geq 2 \) and \(c\) belongs to th...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2023-10
Main Authors: Esparza-Amador, Adrián, Inoquio-Renteria, Irene
Format: Article
Language:English
Subjects:
Formalism
Thermodynamics
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We provide a version of a thermodynamic formalism of entire transcendental maps that exhibit Baker domains, denoted as \(f_{\ell, c}: \mathbb C\to \mathbb C\) and defined by \(f_{\ell, c}(z)= c-(\ell-1)\log c+ \ell z- e^z\), where \(\ell \in \mathbb N\), with \(\ell \geq 2 \) and \(c\) belongs to the disk \( D(\ell, 1)\) in the complex plane. We show in particular the existence and uniqueness of conformal measures and that the Hausdorff dimension is the unique zero of the pressure function \(t\to P(t)\), for \(t>1,\) where \(J_r(f)\) is the radial Julia set.
ISSN:2331-8422