Connectivity of the Julia sets of singularly perturbed rational maps

doi:10.1007/s12044-019-0478-8

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	Connectivity of the Julia sets of singularly perturbed rational maps
	Fu, Jianxun 1; Zhang, Yanhua 2
	2019-06-01
发表期刊	PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES
ISSN	0253-4142
卷号	129 期号:3 页码:8
摘要	We consider a family of rational functions which is given by f(lambda)(z) = z(n)(z(2n) - lambda(n+1))/z(2n) - lambda(3n-1), where n >= 2 and lambda is an element of C* - {lambda : lambda(2n-2) = 1}. When lambda not equal 0 is small, f(lambda) can be seen as a perturbation of the unicritical polynomial z bar right arrow z(n). It was known that in this case the Julia set J (f(lambda)) of f(lambda) is a Cantor set of circles on which the dynamics of f(lambda) is not topologically conjugate to that of any McMullen maps. In this paper, we prove that this is the unique case such that J (f(lambda)) is disconnected.
关键词	Julia sets connectivity Herman ring Cantor circles
DOI	10.1007/s12044-019-0478-8
语种	英语
资助项目	National Natural Science Foundation of China[11401298]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000464842100003
出版者	SPRINGER INDIA
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34563
专题	中国科学院数学与系统科学研究院
通讯作者	Fu, Jianxun
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Qufu Normal Univ, Dept Math, Qufu 273165, Peoples R China
推荐引用方式 GB/T 7714	Fu, Jianxun,Zhang, Yanhua. Connectivity of the Julia sets of singularly perturbed rational maps[J]. PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES,2019,129(3):8.
APA	Fu, Jianxun,&Zhang, Yanhua.(2019).Connectivity of the Julia sets of singularly perturbed rational maps.PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES,129(3),8.
MLA	Fu, Jianxun,et al."Connectivity of the Julia sets of singularly perturbed rational maps".PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES 129.3(2019):8.