On the distribution of Julia sets of holomorphic maps

doi:10.1007/s10473-020-0401-5

CSpace

	On the distribution of Julia sets of holomorphic maps
	Cao, Chunlei 1; Wang, Yuefei 2,3
	2020-07-01
发表期刊	ACTA MATHEMATICA SCIENTIA
ISSN	0252-9602
卷号	40 期号:4 页码:903-909
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.
关键词	Fatou set Julia set transcendental analytic map free Jordan arc
DOI	10.1007/s10473-020-0401-5
收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000538841600001
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51633
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Yuefei
作者单位	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
推荐引用方式 GB/T 7714	Cao, Chunlei,Wang, Yuefei. On the distribution of Julia sets of holomorphic maps[J]. ACTA MATHEMATICA SCIENTIA,2020,40(4):903-909.
APA	Cao, Chunlei,&Wang, Yuefei.(2020).On the distribution of Julia sets of holomorphic maps.ACTA MATHEMATICA SCIENTIA,40(4),903-909.
MLA	Cao, Chunlei,et al."On the distribution of Julia sets of holomorphic maps".ACTA MATHEMATICA SCIENTIA 40.4(2020):903-909.