Area and Hausdorff dimension of Sierpiski carpet Julia sets

被引：2

作者：

Fu, Yuming ^{[1
]}

Yang, Fei ^{[1
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

来源：

MATHEMATISCHE ZEITSCHRIFT | 2020年 / 294卷 / 3-4期

基金：

中国国家自然科学基金;

关键词：

Sierpiski carpet; Julia set; Positive area; Hausdorff dimension; QUASI-SYMMETRIC GEOMETRY; SIEGEL DISKS; SIERPINSKI; DYNAMICS; BOUNDARY; RIGIDITY;

D O I：

10.1007/s00209-019-02319-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the existence of rational maps whose Julia sets are Sierpiski carpets having positive area. Such rational maps can be constructed such that they either contain a Cremer fixed point, a Siegel disk or are infinitely renormalizable. We also construct some Sierpiski carpet Julia sets with zero area but with Hausdorff dimension two. Moreover, for any given number s is an element of(1,2), we prove the existence of Sierpiski carpet Julia sets having Hausdorff dimension exactly s.

引用

页码：1441 / 1456

页数：16