Local connectivity of Julia sets for unicritical polynomials

• 成果类型: Article
• 署名作者: Kahn, Jeremy; Lyubich, Mikhail
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.170.413
• 发表日期: 2009
• 页码: 413-426
• 关键词: dynamics

摘要

We prove that the Julia set J(f) of at most finitely renormalizable unicritical polynomial f : z bar right arrow z(d) + c with all periodic points repelling is locally connected. (For d = 2 it was proved by Yoccoz around 1990.) It follows from a priori bounds in a modified Principal Nest of puzzle pieces. The proof of a priori bounds makes use of new analytic tools developed in [KL09] that give control of moduli of annuli under maps of high degree.