AI 中文总结
本文研究Hénon映射逃逸集及相关格林函数超水平集的自同构，得到逃逸集自同构的局部标准型，刻画了保持逃逸集的$\text{C}^2$整体自同构，还描述了格林函数超水平集的自同构。
AI 中文摘要
本文的研究目的有两个。首先，我们得到了Hénon映射逃逸集在无穷远吸引不动点邻域内自同构的标准型。在该局部描述的基础上，我们刻画了保持逃逸集的$\boldsymbol{\text{C}^2}$整体自同构。由Hubbard--Oberste-Vorth（文献[HOV]）建立的逃逸集解析结构，在这些结果的证明中起到了关键作用。类似地，我们研究了与Hénon映射相关的格林函数超水平集的解析结构，并给出了这些区域自同构的描述。
英文摘要
The aim of this article is two-fold. First, we obtain a normal form for automorphisms of the escaping sets of Hénon maps in a neighborhood of the attracting fixed point at infinity. Building on this local description, we characterize the global automorphisms of $\mathbb{C}^2$ that preserve the escaping sets. The analytic structure of the escaping sets, as established by Hubbard--Oberste-Vorth (\cite{HOV}), plays a crucial role in the proof of these results. In a similar spirit, we investigate the analytic structure of the super-level sets of the Green's functions associated with Hénon maps and give a description of the automorphisms of these domains.
