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首页> 外文期刊>Revue Roumaine de Mathematiques Pures et Appliquees >COLOR VISUALIZATION OF BLASCHKE SELF-MAPPINGS OF THE REAL PROJECTIVE PLANE
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COLOR VISUALIZATION OF BLASCHKE SELF-MAPPINGS OF THE REAL PROJECTIVE PLANE

机译：实射影平面的Blaschke自映射的颜色可视化

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摘要

The real projective plane 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 C. It is known that the only analytic bijective self-mappings of 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 precisely, 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. Additional graphics and animations are provided on the web site of the project [1]. On the website the reader can also find the color version of the article.
机译：真实的投影平面P〜2可以具有解析结构，使其成为不可定向的Klein曲面。该表面的双解析自映射是Riemann球体C的解析自映射的投影。已知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变换获得的。它们不再是一对一的映射。但是，其中一些产品可以投影到P〜2上，它们成为P〜2的解析自映射。更准确地说，它们表示P〜2上不可定向的分支覆盖Klein表面的规范投影。本文致力于此类映射的颜色可视化。工作工具是我们在之前的论文中介绍的同时延续技术。在项目的网站上提供了其他图形和动画[1]。读者还可以在网站上找到文章的彩色版本。

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