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arXiv 2004.05420math.CVmath.DS
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具有有界wandering domains的$\mathbb{C}^m$的自同构

Automorphisms of $\mathbb{C}^m$ with bounded wandering domains

Luka Boc Thaler

摘要:

我们证明了欧氏球可以实现为$\mathbb{C}^m$的全纯自同构的Fatou分量,特别是作为逃逸和振荡游荡域。此外,对于一大类有界域也是如此,即对于所有闭包是多项式凸的有界正则开集$Ω\subset \mathbb{C}^m$也是如此。我们的结果给出了特别是第一个例子的有界Fatou组件的光滑边界的全纯自同构的范畴。

英文摘要:

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.

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