Proof of the Branner-Hubbard conjecture on Cantor Julia sets
نویسندگان
چکیده
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 filledin Julia set containing critical points is aperiodic. This result was a conjecture raised by Branner and Hubbard in 1992.
منابع مشابه
§2. Polynomials for which All But One of the Critical Orbits Escape
Introduction The following notes provide an introduction to recent work of Branner, Hubbard and Yoccoz on the geometry of polynomial Julia sets. They are an expanded version of lectures given in Stony Brook in Spring 1992. I am indebted to help from the audience. Section 1 describes unpublished work by J.-C. Yoccoz on local connectivity of quadratic Julia sets. It presents only the " easy " par...
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