Examples of codification of the dynamics of a rational function into a topological tree

• Main Authors: Laura Cano, Patricia Domínguez, Josué Vázquez
• Format: Article
• Language: Spanish
• Published: Universidad Industrial de Santander 2020-01-01
• Series: Revista Integración
• Subjects: Graph; Holomorphic Dynamics; Herman rings; Quasi-conformal surgery
• Online Access: https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/10330

In 1736 L. Euler gave solution to the famous Seven Bridges of Königsberg problem, considerin a graph consisting of nodes representing the landmasses and arcs representing the bridges. This problem is a referent of how to codify the information given of a problem into a simpler and richer structure. In the case of the Dynamics of rational functions, Shishikura in [5] explores this idea in the context of rational functions, and he stated a connection between a certain kind of topological tree with a p-cycle of Herman rings associated to a rational function. In this work we develop some examples of realizable configurations for rational functions, two of them sketched in [5], and an example of a non realizable configuration which we modify in order to be realizable.