Transcendental Julia Sets of Minimal Hausdorff Dimension

2021/09/10 by Burkart, Jack, Lazebnik, Kirill · 1 citation
#30D05 #37F10 #37F35 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.05001

Abstract

We show the existence of transcendental entire functions f: ℂ → ℂ with Hausdorff-dimension 1 Julia sets, such that every Fatou component of f has infinite inner connectivity. We also show that there exist singleton complementary components of any Fatou component of f, answering a question of Rippon and Stallard (arXiv:1703.11001). Our proof relies on a quasiconformal-surgery approach developed in arXiv:2101.04219.

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