{
  "id": "2310.15996",
  "version": "v1",
  "published": "2023-10-24T16:44:56.000Z",
  "updated": "2023-10-24T16:44:56.000Z",
  "title": "Thermodynamic formalism for entire transcendental maps with hyperbolic Baker Domains",
  "authors": [
    "Adrián Esparza-Amador",
    "Irene Inoquio-Renteria"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-24T16:44:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D35",
      "37F10"
    ],
    "keywords": [
      "entire transcendental maps",
      "hyperbolic baker domains",
      "thermodynamic formalism",
      "radial julia set",
      "complex plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}