Transcendental Julia sets with fractional packing dimension

Burkart, Jack

doi:10.1090/ecgd/363

Transcendental Julia sets with fractional packing dimension
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by Jack Burkart

Conform. Geom. Dyn. 25 (2021), 200-252

DOI: https://doi.org/10.1090/ecgd/363

Published electronically: November 16, 2021

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Abstract:

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

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