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Area and Hausdorff dimension of Sierpiński carpet Julia sets.
- Source :
- Mathematische Zeitschrift; Apr2020, Vol. 294 Issue 3/4, p1441-1456, 16p
- Publication Year :
- 2020
-
Abstract
- We prove the existence of rational maps whose Julia sets are Sierpiński 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 Sierpiński carpet Julia sets with zero area but with Hausdorff dimension two. Moreover, for any given number s ∈ (1 , 2) , we prove the existence of Sierpiński carpet Julia sets having Hausdorff dimension exactly s. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00255874
- Volume :
- 294
- Issue :
- 3/4
- Database :
- Complementary Index
- Journal :
- Mathematische Zeitschrift
- Publication Type :
- Academic Journal
- Accession number :
- 142141940
- Full Text :
- https://doi.org/10.1007/s00209-019-02319-4