Hausdorff dimension of escaping sets of meromorphic functions II

被引：1

作者：

Aspenberg, Magnus ^{[1
]}

Cui, Weiwei ^{[1
]}

机构：

[1] Lund Univ, Ctr Math Sci, Box 118, S-22100 Lund, Sweden

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2023年 / 43卷 / 05期

关键词：

meromorphic functions; singular values; Speiser functions; escaping sets; quasiconformal surgery; MAPS;

D O I：

10.1017/etds.2022.5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A function which is transcendental and meromorphic in the plane has at least two singular values. On the one hand, if a meromorphic function has exactly two singular values, it is known that the Hausdorff dimension of the escaping set can only be either 2 or 1/2. On the other hand, the Hausdorff dimension of escaping sets of Speiser functions can attain every number in [0, 2] (cf. [M. Aspenberg and W. Cui. Hausdorff dimension of escaping sets of meromorphic functions. Trans. Amer. Math. Soc. 374(9) (2021), 6145-6178]). In this paper, we show that number of singular values which is needed to attain every Hausdorff dimension of escaping sets is not more than 4.

引用

页码：1471 / 1491

页数：21

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