Color Visualization of Blaschke Self-Mappings of the Real Projective Plan

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 selfmappings of the Riemann sphere Ĉ. It is known that the only analytic bijective self-mappings of Ĉ are the Möbius transformations. The Blaschke products are obtained by multiplying particular Möbius 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 . More exactly, they represent canonical projections of non orientable branched covering Klein surfaces over P . 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].