共形动力学的镜像：反有理映射、反射群、Schwarz反射与对应之间的相互作用
Mirrors of conformal dynamics: Interplay between anti-rational maps, reflection groups, Schwarz reflections, and correspondences
AI总结：
本文综述了反有理映射迭代、Kleinian反射群作用、正交域中Schwarz反射生成的动力学以及代数对应这四类共形动力学分支之间的密切联系，并通过实例和一般结果展示了它们之间的动力学关系及技术工具的应用。
摘要：
本综述的目标是呈现共形动力学四个分支之间的密切联系：反有理映射的迭代、Kleinian反射群的作用、正交域中Schwarz反射生成的动力学以及代数对应。我们首先给出几个Schwarz反射的例子，以及通过反有理映射与反射群的配对得到的代数对应的例子，还有反射群极限集的Julia集实现（包括经典的类Apollonian垫片）。接着，我们通过显式的Schwarz反射参数空间与反有理映射及反射群参数空间之间的动力学关系来补充这些例子。这些内容辅以一系列一般性结果和重要技术工具（如David手术和拉直技术）的说明。我们还收集了上述理论的若干解析应用。
英文摘要：
The goal of this survey is to present intimate interactions between four branches of conformal dynamics: iterations of anti-rational maps, actions of Kleinian reflection groups, dynamics generated by Schwarz reflections in quadrature domains, and algebraic correspondences. We start with several examples of Schwarz reflections as well as algebraic correspondences obtained by matings between anti-rational maps and reflection groups, and examples of Julia set realizations for limit sets of reflection groups (including classical Apollonian-like gaskets). We follow up these examples with dynamical relations between explicit Schwarz reflection parameter spaces and parameter spaces of anti-rational maps and of reflection groups. These are complemented by a number of general results and illustrations of important technical tools, such as David surgery and straightening techniques. We also collect several analytic applications of the above theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
