Julia Sets, Jordan Curves and Quasi-circles

IF 0.6 4区数学 Q3 MATHEMATICS

Computational Methods and Function Theory Pub Date : 2023-11-30 DOI:10.1007/s40315-023-00512-5

Norbert Steinmetz

引用次数: 0

Abstract

In this paper, the classification of rational functions whose Julia sets are Jordan arcs or curves, which started in (Carleson and Gamelin in Complex dynamics, Springer, Berlin, 1993; Steinmetz in Math Ann 307:531–541, 1997), will be completed. The method of proof is based on two quasi-conformal surgery procedures, which enables shifting the critical points in simply connected (super-)attracting and parabolic basins into a single critical point of highest possible multiplicity.

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茱莉亚集，乔丹曲线和准圆

本文从Carleson和Gamelin In Complex dynamics, Springer, Berlin, 1993开始，讨论Julia集为Jordan弧或曲线的有理函数的分类;Steinmetz in Math Ann 307:531-541, 1997)，将完成。证明方法是基于两个准适形手术程序，这使得在单连通(超)吸引和抛物面盆地的临界点转移到一个最高可能的多重的单一临界点。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Methods and Function Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： CMFT is an international mathematics journal which publishes carefully selected original research papers in complex analysis (in a broad sense), and on applications or computational methods related to complex analysis. Survey articles of high standard and current interest can be considered for publication as well.