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Proof of the Branner-Hubbard conjucture on Cantor Julia sets

Weiyuan Qiu·Yongcheng Yin
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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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Weiyuan Qiu, Yongcheng Yin. 2006-08-02. Proof of the Branner-Hubbard conjucture on Cantor Julia sets. https://arxiv.org/abs/math/0608045

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