Proof of the Branner-Hubbard conjucture on Cantor Julia sets

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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.
29 pages, 15 figures

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Dynamical Systems, 37F10; 37F20

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http://salesiana.dossiersoluciones.com/handle/123456789/115248

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0608045
 http://arxiv.org/abs/math/0608045

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arXiv