Transcendental Julia Sets of Minimal Hausdorff Dimension
Complex Variables
2025-07-09 v1 Dynamical Systems
Abstract
We show the existence of transcendental entire functions with Hausdorff-dimension Julia sets, such that every Fatou component of has infinite inner connectivity. We also show that there exist singleton complementary components of any Fatou component of , answering a question of Rippon and Stallard (arXiv:1703.11001). Our proof relies on a quasiconformal-surgery approach developed in arXiv:2101.04219.
Keywords
Cite
@article{arxiv.2109.05001,
title = {Transcendental Julia Sets of Minimal Hausdorff Dimension},
author = {Jack Burkart and Kirill Lazebnik},
journal= {arXiv preprint arXiv:2109.05001},
year = {2025}
}