Combinatorial rigidity for unicritical polynomials

• 成果类型: Article
• 署名作者: Avila, Artur; Kahn, Jeremy; Lyubich, Mikhail; Shen, Weixiao
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.170.783
• 发表日期: 2009
• 页码: 783-797
• 关键词: local connectivity; mandelbrot; DYNAMICS; families; sets

摘要

We prove that any unicritical polynomial f(c) : z bar right arrow z(d) + c which is at most finitely renormalizable and has only repelling periodic points is combinatorially rigid. This implies that the connectedness locus (the Multibrot set) is locally connected at the corresponding parameter values and generalizes Yoccoz's Theorem for quadratics to the higher degree case.