Thermodynamic formalism of transcendental entire maps of finite singular type |
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Authors: | Ion Coiculescu Bartłomiej Skorulski |
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Institution: | (1) The College of Saint Rose, Albany, NY, USA;(2) Universidad Católica del Norte, Antofagasta, Chile;(3) Warsaw University of Technology, Poland |
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Abstract: | We build a version of a thermodynamic formalism for maps
of the form f(z) = ∑
j = 0
p + q
a
j
e
(j−p)z
where p, q > 0 and
. We show in particular the existence and uniqueness of (t,α)-conformal measures and that the Hausdorff dimension HD(J
f
r
) = h is the unique zero of the pressure function t ↦ P(t) for t > 1, where the set J
f
r
is the radial Julia set.
Partially supported by NSF Grant DMS 0100078.
Partially supported by Warsaw University of Technology Grant No. 504G11200023000, Polish KBN Grant No. 2PO3A03425 and Chilean
FONDECYT Grant No. 11060280. |
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Keywords: | 2000 Mathematics Subject Classification: 37F35 37D35 37F10 30D05 |
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