论文标题
驯服多项式无穷大的盆地
The basin of infinity of tame polynomials
论文作者
论文摘要
令$ \ mathbb {c} _v $为一个特征零代数封闭字段，相对于非架构的绝对值已完成。我们为在$ \ mathbb {c} _v [z] $ $ d \ ge 2 $中提供了两个驯服多项式的必要条件，以分析其无限盆地。在一元中心多项式的空间中，驯服多项式及其在无穷大盆地中的所有临界点形成了驯服位点。我们表明，tame Map $ f \ in \ mathbb {c} _v [z] $在且仅当$ f $的fatou集与Infinity的盆地重合时，才会关闭Tame Shift locus。
Let $\mathbb{C}_v$ be a characteristic zero algebraically closed field which is complete with respect to a non-Archimedean absolute value. We provide a necessary and sufficient condition for two tame polynomials in $\mathbb{C}_v[z]$ of degree $d \ge 2$ to be analytically conjugate on their basin of infinity. In the space of monic centered polynomials, tame polynomials with all their critical points in the basin of infinity form the tame shift locus. We show that a tame map $f\in\mathbb{C}_v[z]$ is in the closure of the tame shift locus if and only if the Fatou set of $f$ coincides with the basin of infinity.
