ESCAPE QUARTERED THEOREM AND THE CONNECTIVITY OF THE JULIA SETS OF A FAMILY OF RATIONAL MAPS

doi:10.3934/dcds.2019211

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	ESCAPE QUARTERED THEOREM AND THE CONNECTIVITY OF THE JULIA SETS OF A FAMILY OF RATIONAL MAPS
	Wang, Youming 1,2; Yang, Fei 1; Zhang, Song 3; Liao, Liangwen 1
	2019-09-01
发表期刊	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
ISSN	1078-0947
卷号	39 期号:9 页码:5185-5206
摘要	In this paper, we investigate the dynamics of the following family of rational maps f(lambda) (z) = z(2n) - 3(n+1) z(n) (z(2n) - lambda(n-1)) with one parameter lambda is an element of C* -{lambda:lambda(2n+2) =1}, where n >= 2. This family of rational maps is viewed as a singular perturbation of the bi- critical map P-n (z) = z(-n) if lambda not equal 0 is small. It is proved that the Julia set J (f(lambda)) is either a quasicircle, a Cantor set of circles, a Sierpinski carpet or a degenerate Sierpinski carpet provided the free critical orbits of f(lambda) are attracted by the super-attracting cycle 0 <-> 1. Furthermore, we prove that there exists suitable lambda such that J (f(lambda)) is a Cantor set of circles but the dynamics of f(lambda) on J (f(lambda)) is not topologically conjugate to that of any known rational maps with only one or two free critical orbits (including McMullen maps and the generalized McMullen maps). The connectivity of J (f(lambda)) is also proved if the free critical orbits are not attracted by the cycle 0 $ 1. Finally we give an estimate of the Hausdor ff dimension of the Julia set of f(lambda) in some special cases.
关键词	Singular perturbation Julia sets Cantor circles connectivity Hausdorff dimension
DOI	10.3934/dcds.2019211
语种	英语
资助项目	NSFC[11671092] ; NSFC[11671191] ; NSFC[11871208] ; Scientific Research Foundation of Hunan Provincial Education Department[16C0763] ; Natural Science Foundation of Hunan Province[2018JJ2159] ; Fundamental Research Funds for the Central Universities[0203-14380022] ; Fundamental Research Funds for the Central Universities[0203-14380025]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000469023800011
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34905
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Youming
作者单位	1.Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China 2.Hunan Agr Univ, Dept Appl Math, Changsha 410128, Hunan, 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	Wang, Youming,Yang, Fei,Zhang, Song,et al. ESCAPE QUARTERED THEOREM AND THE CONNECTIVITY OF THE JULIA SETS OF A FAMILY OF RATIONAL MAPS[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2019,39(9):5185-5206.
APA	Wang, Youming,Yang, Fei,Zhang, Song,&Liao, Liangwen.(2019).ESCAPE QUARTERED THEOREM AND THE CONNECTIVITY OF THE JULIA SETS OF A FAMILY OF RATIONAL MAPS.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,39(9),5185-5206.
MLA	Wang, Youming,et al."ESCAPE QUARTERED THEOREM AND THE CONNECTIVITY OF THE JULIA SETS OF A FAMILY OF RATIONAL MAPS".DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 39.9(2019):5185-5206.