Transcendental Julia sets of minimal Hausdorff dimension

被引：0

作者：

Burkart, Jack ^{[1
]}

Lazebnik, Kirill ^{[2
]}

机构：

[1] Bard Coll Simons Rock, 84 Alford Rd, Great Barrington, MA 01230 USA

[2] Univ Texas Dallas, Dept Math Sci, 800 W Campbell Rd, Richardson, TX 75080 USA

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2025年

关键词：

complex dynamics; dimension; interpolation; Julia sets; CONNECTED WANDERING DOMAINS;

D O I：

10.1017/etds.2024.124

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show the existence of transcendental entire functions f: C -> C with Hausdorff-dimension 11 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 [Eremenko points and the structure of the escaping set. Trans. Amer. Math. Soc. 372(5) (2019), 3083-3111]. Our proof relies on a quasiconformal-surgery approach developed by Burkart and Lazebnik [Interpolation of power mappings. Rev. Mat. Iberoam. 39(3) (2023), 1181-1200].

引用

页数：73

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