Proof of the Branner-Hubbard conjecture on Cantor Julia sets

By Weiyuan Qiu, Yongcheng Yin. 2006

88 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/acf02d9191e533dfdd53f106d050c41898d9f6fe

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Yongcheng Yin
2. Weiyuan Qiu

In Mathematical Physics

1. Weiyuan Qiu
2. Xiaoguang Wang
3. Yongcheng Yin

In Statistical and Nonlinear Physics

1. Xiaoguang Wang
2. Yongcheng Yin
3. Weiyuan Qiu

Citations in the corpus

• Dynamics of McMullen maps (2012, background): “Applications of tableaux analysis combined with puzzle techniques can be found in [2], [14], [21], [22], [25], [26], [27], [32] and many other papers.”