Equivalence between subshrubs and chaotic bands in the Mandelbrot set
We study in depth the equivalence between subshrubs and chaotic bands in the Mandelbrot set. In order to do so, we introduce the rules for chaotic bands and the rules for subshrubs, as well as the transformation rules that allow us to interchange them. From all the denominations of a chaotic band, w...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/DDNS/2006/70471 |
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| _version_ | 1832549521488347136 |
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| author | G. Pastor M. Romera G. Alvarez D. Arroyo F. Montoya |
| author_facet | G. Pastor M. Romera G. Alvarez D. Arroyo F. Montoya |
| author_sort | G. Pastor |
| collection | DOAJ |
| description | We study in depth the equivalence between subshrubs and chaotic
bands in the Mandelbrot set. In order to do so, we introduce the
rules for chaotic bands and the rules for subshrubs, as well as
the transformation rules that allow us to interchange them. From
all the denominations of a chaotic band, we show the canonical
form; that is, the one associated to the hyperbolic component that
generates such a chaotic band. Starting from the study of the
one-dimensional route, we fulfil an inductive study that gives a
generalization of the shrub concept. |
| format | Article |
| id | doaj-art-6f3db710e9ef4be4a8a00416eaa1c55f |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-6f3db710e9ef4be4a8a00416eaa1c55f2025-02-03T06:11:10ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2006-01-01200610.1155/DDNS/2006/7047170471Equivalence between subshrubs and chaotic bands in the Mandelbrot setG. Pastor0M. Romera1G. Alvarez2D. Arroyo3F. Montoya4Departamento de Tratamiento de la Informacin y Codificacin, Instituto de Física Aplicada, Consejo Superior de Investigaciones Científicas, Serrano 144, Madrid 28006, SpainDepartamento de Tratamiento de la Informacin y Codificacin, Instituto de Física Aplicada, Consejo Superior de Investigaciones Científicas, Serrano 144, Madrid 28006, SpainDepartamento de Tratamiento de la Informacin y Codificacin, Instituto de Física Aplicada, Consejo Superior de Investigaciones Científicas, Serrano 144, Madrid 28006, SpainDepartamento de Tratamiento de la Informacin y Codificacin, Instituto de Física Aplicada, Consejo Superior de Investigaciones Científicas, Serrano 144, Madrid 28006, SpainDepartamento de Tratamiento de la Informacin y Codificacin, Instituto de Física Aplicada, Consejo Superior de Investigaciones Científicas, Serrano 144, Madrid 28006, SpainWe study in depth the equivalence between subshrubs and chaotic bands in the Mandelbrot set. In order to do so, we introduce the rules for chaotic bands and the rules for subshrubs, as well as the transformation rules that allow us to interchange them. From all the denominations of a chaotic band, we show the canonical form; that is, the one associated to the hyperbolic component that generates such a chaotic band. Starting from the study of the one-dimensional route, we fulfil an inductive study that gives a generalization of the shrub concept.http://dx.doi.org/10.1155/DDNS/2006/70471 |
| spellingShingle | G. Pastor M. Romera G. Alvarez D. Arroyo F. Montoya Equivalence between subshrubs and chaotic bands in the Mandelbrot set Discrete Dynamics in Nature and Society |
| title | Equivalence between subshrubs and chaotic bands in the Mandelbrot set |
| title_full | Equivalence between subshrubs and chaotic bands in the Mandelbrot set |
| title_fullStr | Equivalence between subshrubs and chaotic bands in the Mandelbrot set |
| title_full_unstemmed | Equivalence between subshrubs and chaotic bands in the Mandelbrot set |
| title_short | Equivalence between subshrubs and chaotic bands in the Mandelbrot set |
| title_sort | equivalence between subshrubs and chaotic bands in the mandelbrot set |
| url | http://dx.doi.org/10.1155/DDNS/2006/70471 |
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