Proof of the Branner-Hubbard conjucture on Cantor Julia sets

2006/08/02 by Qiu, Weiyuan, Yin, Yongcheng · 6 citations
#37F10 #37F20 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0608045

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.

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