Proof of the Branner-Hubbard conjucture on Cantor Julia sets
Dynamical Systems
2007-05-23 v1
Abstract
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 the Julia set of a polynomial is a Cantor set if and only if each component of the filled-in Julia set containing critical points is aperiodic. This result was a conjecture raised by Branner and Hubbard in 1992.
Keywords
Cite
@article{arxiv.math/0608045,
title = {Proof of the Branner-Hubbard conjucture on Cantor Julia sets},
author = {Weiyuan Qiu and Yongcheng Yin},
journal= {arXiv preprint arXiv:math/0608045},
year = {2007}
}
Comments
29 pages, 15 figures