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.References
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Bibliographic Information
- Jack Burkart
- Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706
- MR Author ID: 1317293
- ORCID: 0000-0002-5800-6232
- Email: burkart2@wisc.edu
- Received by editor(s): August 26, 2019
- Received by editor(s) in revised form: July 8, 2020, and March 9, 2021
- Published electronically: November 16, 2021
- © Copyright 2021 American Mathematical Society
- Journal: Conform. Geom. Dyn. 25 (2021), 200-252
- MSC (2020): Primary 37C45, 37F10
- DOI: https://doi.org/10.1090/ecgd/363
- MathSciNet review: 4340830