Abstract

CANO, Laura; DOMINGUEZ, Patricia  and  VAZQUEZ, Josué. Examples of codification of the dynamics of a rational function into a topological tree. Integración - UIS [online]. 2020, vol.38, n.1, pp.1-14.  Epub Feb 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.

Keywords : Graph; Holomorphic Dynamics; Herman rings; Quasi-conformal surgery..

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