Examples of codification of the dynamics of a rational function into a topological tree
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....
| Main Authors: | , , |
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| Format: | Article |
| Language: | Spanish |
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Universidad Industrial de Santander
2020-01-01
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| Series: | Revista Integración |
| Subjects: | |
| Online Access: | https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/10330 |
| _version_ | 1819035757452460032 |
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| author | Laura Cano Patricia Domínguez Josué Vázquez |
| author_facet | Laura Cano Patricia Domínguez Josué Vázquez |
| author_sort | Laura Cano |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-21T07:54:42Z |
| format | Article |
| id | doaj.art-245a99879adb43b88f63a33f506e7d3e |
| institution | Directory Open Access Journal |
| issn | 0120-419X 2145-8472 |
| language | Spanish |
| last_indexed | 2024-12-21T07:54:42Z |
| publishDate | 2020-01-01 |
| publisher | Universidad Industrial de Santander |
| record_format | Article |
| series | Revista Integración |
| spelling | doaj.art-245a99879adb43b88f63a33f506e7d3e2022-12-21T19:11:00ZspaUniversidad Industrial de SantanderRevista Integración0120-419X2145-84722020-01-01381Examples of codification of the dynamics of a rational function into a topological treeLaura Cano0Patricia Domínguez1Josué Vázquez2Benemérita Universidad Autónoma de Puebla, Facultad de Ciencias Físico-Matemáticas, Puebla, México.Benemérita Universidad Autónoma de Puebla, Facultad de Ciencias Físico-Matemáticas, Puebla, México.Benemérita Universidad Autónoma de Puebla, Facultad de Ciencias Físico-Matemáticas, Puebla, México.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.https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/10330GraphHolomorphic DynamicsHerman ringsQuasi-conformal surgery |
| spellingShingle | Laura Cano Patricia Domínguez Josué Vázquez Examples of codification of the dynamics of a rational function into a topological tree Revista Integración Graph Holomorphic Dynamics Herman rings Quasi-conformal surgery |
| title | Examples of codification of the dynamics of a rational function into a topological tree |
| title_full | Examples of codification of the dynamics of a rational function into a topological tree |
| title_fullStr | Examples of codification of the dynamics of a rational function into a topological tree |
| title_full_unstemmed | Examples of codification of the dynamics of a rational function into a topological tree |
| title_short | Examples of codification of the dynamics of a rational function into a topological tree |
| title_sort | examples of codification of the dynamics of a rational function into a topological tree |
| topic | Graph Holomorphic Dynamics Herman rings Quasi-conformal surgery |
| url | https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/10330 |
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