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Julia集及其Hausdorff维数的连续性
庄伟
2004
Source Publication数学学报
ISSN0583-1431
Volume047Issue:006Pages:1161
Abstract对于d≥2,考虑多项式族Pc=z^d+c,c∈C.Kc={z∈C|{Pc^n(z)}n≥0有界}为Pc的填充Julia集,Jc=ЭKc为其Julia集.HD(Jc)为Jc的Hausdorff维数.设ω(0)为Pco的临界点0的轨道的聚点集.我们假定Pco在ω(0)上是扩张的,且0∈Jco,|c0|>ε>0.如果一序列cn→co,则Jcn→Jco,Kcn→Jco,在Hausdorff拓扑下.如果存在一常数C1>0和一序列cn→co,使得d(cn,Jco)≥C1|cn-co|^1+1/d,则HD(Jcn)→HD(Jco).这里d(cn,Jco)为Cn与Jco间距离.
Language英语
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/42141
Collection中国科学院数学与系统科学研究院
Affiliation中国科学院数学与系统科学研究院
Recommended Citation
GB/T 7714
庄伟. Julia集及其Hausdorff维数的连续性[J]. 数学学报,2004,047(006):1161.
APA 庄伟.(2004).Julia集及其Hausdorff维数的连续性.数学学报,047(006),1161.
MLA 庄伟."Julia集及其Hausdorff维数的连续性".数学学报 047.006(2004):1161.
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