Revista Integración
ISSN 0120-419X ISSN 2145-8472
CANO, Laura; DOMINGUEZ, Patricia VAZQUEZ, Josué. Examples of codification of the dynamics of a rational function into a topological tree. []. , 38, 1, pp.1-14. 27--2020. ISSN 0120-419X. https://doi.org/10.18273/revint.v38n1-2020001.
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.
MSC2010: 37F10, 32H50, 30D05, 32H50.
: Graph; Holomorphic Dynamics; Herman rings; Quasi-conformal surgery..