We construct polynomial automorphisms with wandering Fatou components. The four-dimensional automorphisms H lie in a one-parameter family, depending on the parameter $\delta \in \mathbb{C}\setminus \{0\}$, and as $\delta \to 0$ the automorphisms degenerate to the two-dimensional polynomial map P constructed in [2]. Our main result states that if P has a wandering domain, then H does too for δ sufficiently small.

中文翻译：

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游荡的Fatou分量的多项式自同构。

我们构造带有游荡的Fatou分量的多项式自同构。取决于参数，四维自同构H处于一参数族$\delta \in \mathbb{C}\setminus \{0\}$， 并作为 $\delta \to 0$自同构性退化为[2]中构造的二维多项式图P。我们的主要结果表明，如果P具有漂移域，则H对于δ足够小也是如此。