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

共 50 条

[41] Locally Sierpinski Julia sets of Weierstrass elliptic functions
Hawkins, Jane M.
Look, Daniel M.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2006, 16 (05): : 1505 - 1520
[42] Hyperbolic Julia Sets are Poly-Time Computable
Braverman, Mark
ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE, 2005, 120 : 17 - 30
[43] Connectivity properties of Julia sets of Weierstrass elliptic functions
Hawkins, J
Koss, L
TOPOLOGY AND ITS APPLICATIONS, 2005, 152 (1-2) : 107 - 137
[44] Ergodic properties and Julia sets of Weierstrass elliptic functions
Hawkins, J
Koss, L
MONATSHEFTE FUR MATHEMATIK, 2002, 137 (04): : 273 - 300
[45] Unveiling the fractal structure of Julia sets with Lagrangian descriptors
Garcia-Garrido, Victor J.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2020, 91
[46] JULIA SETS ON RP2 AND DIANALYTIC DYNAMICS
Goodman, Sue
Hawkins, Jane
CONFORMAL GEOMETRY AND DYNAMICS, 2014, 18 : 85 - 109
[47] A FUNDAMENTAL DICHOTOMY FOR JULIA SETS OF A FAMILY OF ELLIPTIC FUNCTIONS
Koss, L.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 137 (11) : 3927 - 3938
[48] BACKWARD ITERATION ALGORITHMS FOR JULIA SETS OF MOBIUS SEMIGROUPS
Stankewitz, Rich
Semi, Hiroki
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (11) : 6475 - 6485
[49] Hausdorff measure of escaping sets on certain meromorphic functions
Li, Wenli
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 461 (02) : 1471 - 1497
[50] Entire functions whose Julia sets include any finitely many copies of quadratic Julia sets
Katagata, Koh
NONLINEARITY, 2017, 30 (06) : 2360 - 2380

← 1 2 3 4 5 →