Zalcman functions and similarity between the Mandelbrot set, Julia sets, and the tricorn

被引：2

作者：

Kawahira, Tomoki ^{[1
,2
]}

机构：

[1] Tokyo Inst Technol, Dept Math, Tokyo 1528551, Japan

[2] RIKEN Ctr Adv Intelligence Project AIP, Math Sci Team, Chuo Ku, 1-4-1 Nihonbashi, Tokyo 1030027, Japan

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2020年 / 10卷 / 02期

关键词：

HAUSDORFF DIMENSION; MULTICORNS; DYNAMICS;

D O I：

10.1007/s13324-020-00357-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a simple proof of Tan's theorem on asymptotic similarity between the Mandelbrot set and Julia sets at Misiurewicz parameters. Then we give a new perspective on this phenomenon in terms of Zalcman functions, that is, entire functions generated by applying Zalcman's lemma to complex dynamics. We also show asymptotic similarity between the tricorn and Julia sets at Misiurewicz parameters, which is an antiholomorphic counterpart of Tan's theorem.

引用

页数：18

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