论文标题
$ g $ $ cantor套装和德国朱莉娅套装
Genus $g$ Cantor sets and germane Julia sets
论文作者
论文摘要
本文的主要目的是给$ \ mathbb {r}^3 $ as topogical障碍物造成拓扑障碍。我们的主要工具是Cantor套装的属。我们提供了一个新的结构，该属属$ g $ cantor套件是本地属的第一个构建，每个点都为$ g $，然后证明该cantor套件可以实现为朱莉娅（Julia）的朱莉娅（Julia）套件，这是一套均匀的Quasiregular映射。这些是为$ g \ geq 3 $构建的第一个这样的Cantor Julia套装。然后，我们转向动态应用，并表明每座柔毛均匀地图的Cantor Julia套件都有有限的属$ g $；朱莉娅（Cantor Julia）集中的局部属必须发生在朱莉娅（Julia）集合的密集子集中。并且确实存在cantor Julia设置的地方，而本地属是非恒定体的。
The primary aim of this paper is to give topological obstructions to Cantor sets in $\mathbb{R}^3$ being Julia sets of uniformly quasiregular mappings. Our main tool is the genus of a Cantor set. We give a new construction of a genus $g$ Cantor set, the first for which the local genus is $g$ at every point, and then show that this Cantor set can be realized as the Julia set of a uniformly quasiregular mapping. These are the first such Cantor Julia sets constructed for $g\geq 3$. We then turn to our dynamical applications and show that every Cantor Julia set of a hyperbolic uniformly quasiregular map has a finite genus $g$; that a given local genus in a Cantor Julia set must occur on a dense subset of the Julia set; and that there do exist Cantor Julia sets where the local genus is non-constant.
