Hyperbolic dimension and radial Julia sets of transcendental functions

Abstract

We survey the definition of the radial Julia set of a meromorphic function (in fact, more generally, any "Ahlfors islands map"), and give a simple proof that the Hausdorff dimension of the reduced Julia set always coincides with the hyperbolic dimension.

11 pages

References in corpus (1)

• Dynamics of meromorphic functions with direct or logarithmic singularities

Cited by in corpus (13)

• Non-autonomous conformal iterated function systems and Moran-set constructions
• Absence of wandering domains for some real entire functions with bounded singular sets
• Bowen's formula for meromorphic functions
• Lebesgue measure of escaping sets of entire functions of completely regular growth
• Escape rate and Hausdorff measure for entire functions
• Exotic Baker and wandering domains for Ahlfors islands maps
• Non-escaping endpoints do not explode
• On the packing dimension of the Julia set and the escaping set of an entire function
• Dimension rigidity in conformal structures
• Dynamical sets whose union with infinity is connected
• The Hausdorff dimension of Julia sets of meromorphic functions in the Speiser class
• Rigidity and absence of line fields for meromorphic and Ahlfors islands maps
• Fatou's associates