论文标题
2属cantor套装
Genus 2 Cantor sets
论文作者
论文摘要
我们构建一个几何自相似的cantor套装$ x $ of属$ 2 $ in $ \ mathbb {r}^3 $。这种结构是第一个在$ x $的每个点显示本地属的$ 2 $的建筑。作为一个应用程序，我们也是第一次构造了一个均匀的Quasiregular映射$ f：\ mathbb {r}^3 \ to \ mathbb {r}^3 $，julia set $ j（f）$是$ 2 $ $ 2 $ cantor set。
We construct a geometrically self-similar Cantor set $X$ of genus $2$ in $\mathbb{R}^3$. This construction is the first for which the local genus is shown to be $2$ at every point of $X$. As an application, we construct, also for the first time, a uniformly quasiregular mapping $f:\mathbb{R}^3 \to \mathbb{R}^3$ for which the Julia set $J(f)$ is a genus $2$ Cantor set.
