AI 中文总结
综述1958年至2025年可交换超越整函数动力学成果，探讨其函数形式、动力学性质，分析基于点轨道动力学分类的子集关系及逃逸集分类，还讨论了相关集合的动力学关系与蹦极集和游荡域的情况。
AI 中文摘要
本文综述了1958年至2025年可交换超越整函数动力学的重要结果。讨论了可交换的超越整函数形式，以及可交换整函数的动力学性质，如法图集和朱利亚集的关系。还考虑了基于复平面上点轨道动力学分类的子集关系，包括填充朱利亚集\(K(f)\)、逃逸集\(I(f)\)和蹦极集\(BU(f)\)等。逃逸集还按逃逸速度进一步分类，如快速逃逸集\(A(f)\)等。此外，讨论了这些集合的动力学关系，以及蹦极集与游荡域的关系及条件。
英文摘要
In this paper, we survey important results on the dynamics of permutable transcendental entire functions from 1958 to 2025. We have discussed the forms of transcendental entire functions that could be permutable. We have also discussed the dynamical properties of permutable entire functions. For instance, how the Fatou and Julia sets are related. We have also considered the relation of the subsets which are classified based on the dynamics of the orbit of a point in the complex plane. They are the filled Julia set $K(f)$ (set of points whose orbits remain bounded), the escaping set $I(f)$ (set of points whose orbits escape to infinity) and the bungee set $BU(f)$ (set of points which are neither bounded nor escaping to infinity). The escaping set is further classified based on the speed of escape, namely, the fast escaping set $A(f)$ or other sets such as $I_0(f)$ and $T(f)$, whose definitions are mentioned in this article. We have also discussed the dynamical relations of these sets. The bungee set sometimes contains a wandering domain, and in this article we have discussed the dynamical relations and conditions that dictates whether wandering domains exists or if it is contained within the bungee set.
Comments20 pages. Comments are welcome
