论文标题
径向朱莉娅集的拓扑维度
The topological dimension of radial Julia sets
论文作者
论文摘要
我们证明，每当$ a $属于$ f_a $的fatou集合时，$ f_a（z）= e^z+a $的蜿蜒集是同型非理性数字的。这扩展了Vasiliki Evdoridou和Lasse Rempe的最新结果。这意味着$ f_a $的径向朱莉娅集对所有吸引和抛物线参数的拓扑维度为零，包括所有$ a \ in（ - \ infty，-1] $。
We prove that the meandering set for $f_a(z)=e^z+a$ is homeomorphic to the space of irrational numbers whenever $a$ belongs to the Fatou set of $f_a$. This extends recent results by Vasiliki Evdoridou and Lasse Rempe. It implies that the radial Julia set of $f_a$ has topological dimension zero for all attracting and parabolic parameters, including all $a\in (-\infty,-1]$. Similar results are obtained for Fatou's function $f(z)=z+1+e^{-z}$.
