论文标题
吸引多项式偏斜产品的流浪域问题
The wandering domain problem for attracting polynomial skew products
论文作者
论文摘要
最近由Astorg等人构建了徘徊的Fatou组件，用于在射影空间上进行更高维度的全态图。他们的例子是带有抛物线不变线的多项式偏斜产品。在本文中，我们研究了多项式偏斜产品$ f $的流浪域问题，并吸引了不变的线$ l $（这是更常见的情况）。我们表明，如果$ f $是一致的（从某种意义上说，关键曲线具有与$ l $的独特横向交叉点），那么$ l $的$ f $的每个FATOU组成部分都是$ l $的盆地，是$ f | _l $的一维fatou组件的扩展。作为推论，没有流浪的fatou组分。我们还将在其他假设下讨论多政治案例。
Wandering Fatou components were recently constructed by Astorg et al for higher dimensional holomorphic maps on projective spaces. Their examples are polynomial skew products with a parabolic invariant line. In this paper we study this wandering domain problem for polynomial skew product $f$ with an attracting invariant line $L$ (which is the more common case). We show that if $f$ is unicritical (in the sense that the critical curve has a unique transversal intersection with $L$), then every Fatou component of $f$ in the basin of $L$ is an extension of a one-dimensional Fatou component of $f|_L$. As a corollary there is no wandering Fatou component. We will also discuss the multicritical case under additional assumptions.
