On the distribution of Julia sets of holomorphic maps

doi:10.1007/s10473-020-0401-5

	On the distribution of Julia sets of holomorphic maps
	Cao, Chunlei 3; Wang, Yuefei 1,2
刊名	ACTA MATHEMATICA SCIENTIA
	2020-07-01
卷号	40 期号:4 页码:903-909
关键词	Fatou set Julia set transcendental analytic map free Jordan arc
ISSN号	0252-9602
DOI	10.1007/s10473-020-0401-5
英文摘要	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.
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000538841600001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/51632]
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.Shenzhen Univ, Coll Math & Stat, Shenzhen 518060, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Beijing Inst Technol, Sch Math & Stat, Beijing 100081, 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.