AI 中文总结
本研究将Hénon映射逃逸集的描述推广至斜积，构造覆盖空间探究其全局逃逸集的解析结构与双全纯等价性，还研究了以非紧复平面为底的斜积的逃逸区域。
AI 中文摘要
我们研究以合适度量空间为底的Hénon映射的斜积，探究其逃逸集的解析结构。本研究将Hubbard与Oberste-Vorth提出的Hénon映射逃逸集描述推广至斜积，为研究其刚性提供框架。对于紧底空间，我们构造每个纤维逃逸集的中间覆盖空间；当底为闭单位圆盘且族全纯依赖于参数时，我们得到全局逃逸集的类似描述。我们进一步利用该覆盖空间构造研究其全局逃逸集的双全纯等价与底层动力学的关系；最后，对于以非紧底$\boldsymbol{\text{C}}$的斜积，我们考虑对应逃逸区域并探究其解析结构。
英文摘要
We study skew products of Hénon maps fibered over suitable metric spaces and investigate the analytic structure of their escaping sets. Our study extends the description of escaping sets for Hénon maps developed by Hubbard and Oberste-Vorth to skew products and provides a framework for studying their rigidity. For a compact base space, we construct an intermediate covering space of each fiberwise escaping set. When the base is the closed unit disk and the family depends holomorphically on the parameter, we obtain an analogous description of the global escaping set. We further use this covering space construction to study the relationship between biholomorphic equivalences of their global escaping sets and the underlying dynamics. Finally, for skew products over the non-compact base $\mathbb{C}$, we consider the corresponding escaping region and investigate its analytic structure.
