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Title: | Equivalence between subshrubs and chaotic bands in the Mandelbrot set |
Authors: | Pastor, Gerardo; Romera, Miguel; Álvarez Marañón, Gonzalo; Arroyo Guardeño, David CSIC ORCID ; Montoya Vitini, Fausto | Keywords: | Mandelbrot set Chaotic bands Subshrubs Transformation rules One-dimensional route Nonlinear science |
Issue Date: | 13-Mar-2006 | Publisher: | Hindawi Publishing Corporation | Citation: | Discrete Dynamics in Nature and Society 2006: 70471 (2006) | Abstract: | 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. | Description: | 25 pages, 7 figures.-- This is an open access article distributed under the Creative Commons Attribution License. | Publisher version (URL): | http://dx.doi.org/10.1155/DDNS/2006/70471 | URI: | http://hdl.handle.net/10261/8872 | DOI: | 10.1155/DDNS/2006/70471 | ISSN: | 1026-0226 |
Appears in Collections: | (IFA) Artículos |
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