Hyperbolic dimension and radial Julia sets of transcendental functions. (English) Zbl 1214.37036
Summary: We survey the definition of the radial Julia set \( J_r(f)\) of a meromorphic function (in fact, more generally, any Ahlfors islands map), and give a simple proof that the Hausdorff dimension of \( J_r(f)\) and the hyperbolic dimension \( \dim_{\operatorname{hyp}}(f)\) always coincide.
MSC:
| 37F35 | Conformal densities and Hausdorff dimension for holomorphic dynamical systems |
| 37F10 | Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets |
| 30D05 | Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable |
Keywords:
hyperbolic dimension; radial Julia set; iterated function system; entire function; meromorphic function; Ahlfors islands map; Hausdorff dimension; conformal measureReferences:
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