Colour visualization of Blaschke product mappings

Abstract

A visualization of Blaschke product mappings can be obtained by treating them as canonical projections of covering Riemann surfaces and finding fundamental domains and covering transformations corresponding to these surfaces. A working tool is the technique of simultaneous continuation we introduced in previous papers. Here, we are refining this technique for some particular types of Blaschke products, for which coloring pre-images of annuli centered at the origin allow us to describe the mappings with a high degree of fidelity. Additional graphics and animations are provided on the web site of the project [1].