ON THE TOPOLOGY OF WANDERING JULIA COMPONENTS

doi:10.3934/dcds.2011.29.929

CSpace > 数学所

	ON THE TOPOLOGY OF WANDERING JULIA COMPONENTS
	Cui, Guizhen1 ; Peng, Wenjuan1 ; Tan, Lei 2
	2011-03-10
发表期刊	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
ISSN	1078-0947
卷号	29 期号:3 页码:929-952
摘要	It is known that for a rational map f with a disconnected Julia set, the set of wandering Julia components is uncountable. We prove that all but countably many of them have a simple topology, namely having one or two complementary components. We show that the remaining countable subset Sigma is backward invariant. Conjecturally Sigma does not contain an infinite orbit. We give a very strong necessary condition for Sigma to contain an infinite orbit, thus proving the conjecture for many different cases. We provide also two sufficient conditions for a Julia component to be a point. Finally we construct several examples describing different topological structures of Julia components.
关键词	Holomorphic dynamics iteration of rational maps topology of wandering Julia components
DOI	10.3934/dcds.2011.29.929
语种	英语
资助项目	NSF of China[10831004] ; NSF of China[10721061] ; Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences ; China Postdoctoral Science Special Foundation[201003020] ; EU Research Training Network CODY, Conformal Structures and Dynamics
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000284619800012
出版者	AMER INST MATHEMATICAL SCIENCES
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12842
专题	数学所
通讯作者	Cui, Guizhen
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Angers, Dept Math, F-49045 Angers, France
推荐引用方式 GB/T 7714	Cui, Guizhen,Peng, Wenjuan,Tan, Lei. ON THE TOPOLOGY OF WANDERING JULIA COMPONENTS[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2011,29(3):929-952.
APA	Cui, Guizhen,Peng, Wenjuan,&Tan, Lei.(2011).ON THE TOPOLOGY OF WANDERING JULIA COMPONENTS.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,29(3),929-952.
MLA	Cui, Guizhen,et al."ON THE TOPOLOGY OF WANDERING JULIA COMPONENTS".DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 29.3(2011):929-952.