Proof of the Branner-Hubbard conjecture on Cantor Julia sets

被引：56

作者：

Qiu WeiYuan ^{[1
]}

Yin YongCheng ^{[1
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS | 2009年 / 52卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Julia set; Branner-Hubbard conjecture; puzzle; tableau; LOCAL CONNECTIVITY; CUBIC POLYNOMIALS; RATIONAL MAPS; ITERATION; DYNAMICS; COMBINATORICS; TOPOLOGY; RIGIDITY; INTERVAL; BOUNDS;

D O I：

10.1007/s11425-008-0178-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By means of a nested sequence of some critical pieces constructed by Kozlovski, Shen, and van Strien, and by using a covering lemma recently proved by Kahn and Lyubich, we prove that a component of the filled-in Julia set of any polynomial is a point if and only if its forward orbit contains no periodic critical components. It follows immediately that the Julia set of a polynomial is a Cantor set if and only if each critical component of the filled-in Julia set is aperiodic. This result was a conjecture raised by Branner and Hubbard in 1992.

引用

页码：45 / 65

页数：21

共 27 条

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