Monatshefte für Mathematik

, Volume 152, Issue 2, pp 105–123

Thermodynamic formalism of transcendental entire maps of finite singular type

  • Ion Coiculescu
  • Bartłomiej Skorulski
Article

DOI: 10.1007/s00605-007-0497-x

Cite this article as:
Coiculescu, I. & Skorulski, B. Mh Math (2007) 152: 105. doi:10.1007/s00605-007-0497-x

Abstract.

We build a version of a thermodynamic formalism for maps \( f:{\Bbb C}\rightarrow{\Bbb C}\) of the form f(z) = ∑j = 0p + qaje(jp)z where p, q > 0 and \( a_j\in{\Bbb C}\). We show in particular the existence and uniqueness of (t,α)-conformal measures and that the Hausdorff dimension HD(Jfr) = h is the unique zero of the pressure function tP(t) for t > 1, where the set Jfr is the radial Julia set.

2000 Mathematics Subject Classification: 37F35, 37D35; 37F10, 30D05
Key words: Meromorphic dynamics, thermodynamic formalism, conformal measures

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Ion Coiculescu
    • 1
  • Bartłomiej Skorulski
    • 2
    • 3
  1. 1.The College of Saint RoseAlbanyUSA
  2. 2.Universidad Católica del NorteAntofagastaChile
  3. 3.Warsaw University of TechnologyPoland