Transcendental Julia sets with fractional packing dimension

Abstract

We construct transcendental entire functions whose Julia sets have packing dimension in ( 1 , 2 ) (1,2) . These are the first examples where the computed packing dimension is not 1 1 or 2 2 . Our analysis will allow us further show that the set of packing dimensions attained is dense in the interval ( 1 , 2 ) (1,2) , and that the Hausdorff dimension of the Julia sets can be made arbitrarily close to the corresponding packing dimension.