毛茸茸的康托集
Hairy Cantor sets
摘要：
本文引入了一种拓扑对象--毛康托尔集，它在许多方面具有Jordan曲线、康托尔集、Cantor花束、毛Jordan曲线等对象的普遍特征，给出了毛Cantor集的公理化刻画，并证明了平面上任意两个毛Cantor集是环境同胚的.毛康托集出现在研究具有无限多重正化结构的全纯映射的动力学中。他们被用来连接的基本概念多项式的重整化的Douady-Hubbard的算术条件获得的赫尔曼-Yoccoz在研究的动力学解析圆同态。
英文摘要：
We introduce a topological object, called hairy Cantor set, which in many ways enjoys the universal features of objects like Jordan curve, Cantor set, Cantor bouquet, hairy Jordan curve, etc. We give an axiomatic characterisation of hairy Cantor sets, and prove that any two such objects in the plane are ambiently homeomorphic. Hairy Cantor sets appear in the study of the dynamics of holomorphic maps with infinitely many renormalisation structures. They are employed to link the fundamental concepts of polynomial-like renormalisation by Douady-Hubbard with the arithmetic conditions obtained by Herman-Yoccoz in the study of the dynamics of analytic circle diffeomorphisms.
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