实射影平面Blaschke自映射的彩色可视化
Color Visualization of Blaschke Self-Mappings of the Real Projective Plan
摘要：
实射影平面$P^2$可以被赋予一个双解析结构，使其成为一个不可定向的克莱因曲面。该曲面的双解析自映射是黎曼球面$\widehat{\mathbb{C}}$的解析自映射的投影。已知$\widehat{\mathbb{C}}$的唯一解析双射自映射是Moebius变换。Blaschke乘积是通过乘以特定的Moebius变换而获得的。它们不再是一对一的映射。然而，这些产品中的一些可以投影到$P^2$上，它们成为$P^2$的双解析自映射。更确切地说，它们表示$P^2$上不可定向分支覆盖Klein曲面的正则投影。这篇文章致力于这种映射的颜色可视化。工作工具是我们在以前的论文中介绍的同时延拓技术。
英文摘要：
The real projective plan $P^2$ can be endowed with a dianalytic structure making it into a non orientable Klein surface. Dianalytic self-mappings of that surface are projections of analytic self-mappings of the Riemann sphere $\widehat{\mathbb{C}}$. It is known that the only analytic bijective self-mappings of $\widehat{\mathbb{C}}$ are the Moebius transformations. The Blaschke products are obtained by multiplying particular Moebius transformations. They are no longer one-to-one mappings. However, some of these products can be projected on $P^2$ and they become dianalytic self-mappings of $P^2$. More exactly, they represent canonical projections of non orientable branched covering Klein surfaces over $P^2$. This article is devoted to color visualization of such mappings. The working tool is the technique of simultaneous continuation we introduced in previous papers.
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。
