逆多项式象的几何性质
Geometric properties of inverse polynomial images
摘要：
给定次数为$n$的多项式$\T_n$，考虑$\R$和$[-1,1]$的逆像，分别用$\T_n^{-1}(\R)$和$\T_n^{-1}([-1,1])$表示。众所周知，$\T_n^{-1}(\R)$由从$\infty$移动到$\infty$的$n$解析约旦弧组成。本文给出了（1）$\T_n^{-1}([-1,1])$由$ν$解析Jordan弧构成和（2）$\T_n^{-1}([-1,1])$连通的充要条件.
英文摘要：
Given a polynomial $\T_n$ of degree $n$, consider the inverse image of $\R$ and $[-1,1]$, denoted by $\T_n^{-1}(\R)$ and $\T_n^{-1}([-1,1])$, respectively. It is well known that $\T_n^{-1}(\R)$ consists of $n$ analytic Jordan arcs moving from $\infty$ to $\infty$. In this paper, we give a necessary and sufficient condition such that (1) $\T_n^{-1}([-1,1])$ consists of $ν$ analytic Jordan arcs and (2) $\T_n^{-1}([-1,1])$ is connected, respectively.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
