Thermodynamic formalism of transcendental entire maps of finite singular type

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 (j−p)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 t ↦ P(t) for t > 1, where the set J f r is the radial Julia set.