Proof of the Branner-Hubbard conjucture on Cantor Julia sets

Details Proof of the Branner-Hubbard conjucture on Cantor Julia sets Proof of the Branner-Hubbard conjucture on Cantor Julia sets

2006-08-02

arxiv.org/abs/math/0608045v1

Mathematics

Dynamical Systems

29 pages, 15 figures

Scientific paper

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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