论文标题
Mandelbrot设置用于分形$ n $ gons和Power of Power of Power系列
Mandelbrot set for fractal $n$-gons and zeros of power series
论文作者
论文摘要
我们提供了一个框架，以研究有限的子集$ g \ subset \ mathbb {c} $中的系数的零零系列零。我们证明，如果连接了设置的$ g $，则将设备磁盘中的零集连接并在本地连接。此外，我们将此结果应用于Mandelbrot设置$ \ Mathcal {m} _n $的分形$ n $ -gons的研究。我们证明，$ \ Mathcal {M} _n $已连接并为任何$ n $进行本地连接。
We give a framework to study the connectedness of the set of zeros of power series with coefficients in a finite subset $G\subset \mathbb{C}$. We prove that the set of zeros in the unit disk is connected and locally connected if some graph on the set $G$ of coefficients is connected. Furthermore, we apply this result to the study of the Mandelbrot set $\mathcal{M}_n$ for fractal $n$-gons. We prove that $\mathcal{M}_n$ is connected and locally connected for any $n$.
