On the packing dimension of the Julia set and the escaping set of an entire function

Abstract

We show that for large classes of entire functions the Julia set and the escaping set have packing dimension two. For example, this is the case for entire functions which are bounded on a curve tending to infinity. More generally, we show that the result holds under suitable growth conditions involving the minimum and maximum modulus.

19 pages

References in corpus (4)

• Dynamics of meromorphic functions with direct or logarithmic singularities
• Hausdorff dimensions of escaping sets of transcendental entire functions
• Hyperbolic dimension and radial Julia sets of transcendental functions
• On the Hausdorff dimension of the Julia set of a regularly growing entire function

Cited by in corpus (1)

• The escaping set in transcendental dynamics