Hyperbolic dimension and radial Julia sets of transcendental functions

Abstract

We survey the definition of the radial Julia set J r ( f ) 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 ) J_r(f) and the hyperbolic dimension dim hyp ⁡ ( f ) \dim _{\operatorname {hyp}}(f) always coincide.