, Volume 152, Issue 2, pp 105-123
Date: 23 Jul 2007

Thermodynamic formalism of transcendental entire maps of finite singular type

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Abstract.

We build a version of a thermodynamic formalism for maps \( f:{\Bbb C}\rightarrow{\Bbb C}\) of the form f(z) = ∑ j = 0 p + q a j e (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(J f r ) = h is the unique zero of the pressure function tP(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.