On the distribution of Julia sets of holomorphic maps

被引：0

作者：

Cao, Chunlei ^{[1
]}

Wang, Yuefei ^{[2
,3
]}

机构：

[1] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

[2] Shenzhen Univ, Coll Math & Stat, Shenzhen 518060, Peoples R China

[3] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2020年 / 40卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Fatou set; Julia set; transcendental analytic map; free Jordan arc; MEROMORPHIC FUNCTIONS; WANDERING DOMAINS; ITERATION; DYNAMICS;

D O I：

10.1007/s10473-020-0401-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 1965 Baker first considered the distribution of Julia sets of transcendental entire maps and proved that the Julia set of an entire map cannot be contained in any finite set of straight lines. In this paper we shall consider the distribution problem of Julia sets of meromorphic maps. We shall show that the Julia set of a transcendental meromorphic map with at most finitely many poles cannot be contained in any finite set of straight lines. Meanwhile, examples show that the Julia sets of meromorphic maps with infinitely many poles may indeed be contained in straight lines. Moreover, we shall show that the Julia set of a transcendental analytic self-map of C* can neither contain a free Jordan arc nor be contained in any finite set of straight lines.

引用

页码：903 / 909

页数：7