论文标题
$ \ mathbb {C}^m $带有有限徘徊域的自动形态
Automorphisms of $\mathbb{C}^m$ with bounded wandering domains
论文作者
论文摘要
我们证明，欧几里得球可以被视为$ \ mathbb {c}^m $的全态自动形态的fatou组成部分，尤其是逃脱和振荡的徘徊域。此外，对于一大批有界域而言，也是如此，即对于所有有限的常规开放集$ω\ subset \ mathbb {c}^m $，其闭合是多条件上凸的。我们的结果尤其给出了一个有界的FATOU组件的第一个示例，该组件具有平稳的圆形自动形态范围。
We prove that the Euclidean ball can be realized as a Fatou component of a holomorphic automorphism of $\mathbb{C}^m$, in particular as the escaping and the oscillating wandering domain. Moreover, the same is true for a large class of bounded domains, namely for all bounded regular open sets $Ω\subset \mathbb{C}^m$ whose closure is polynomially convex. Our result gives in particular the first example of a bounded Fatou component with a smooth boundary in the category of holomorphic automorphisms.
