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Connectivity of the Julia sets of singularly perturbed rational maps

文献类型：期刊论文

作者Fu, Jianxun2; Zhang, Yanhua1
刊名PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES
出版日期2019-06-01
卷号129期号:3页码:8
关键词Julia sets connectivity Herman ring Cantor circles
ISSN号0253-4142
DOI10.1007/s12044-019-0478-8
英文摘要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.
资助项目National Natural Science Foundation of China[11401298]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000464842100003
出版者SPRINGER INDIA
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/34562]  
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.Qufu Normal Univ, Dept Math, Qufu 273165, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, 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.

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来源：数学与系统科学研究院

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