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Equivalence between subshrubs and chaotic bands in the Mandelbrot set

AuthorsPastor, Gerardo; Romera, Miguel; Álvarez Marañón, Gonzalo; Arroyo Guardeño, David ; Montoya Vitini, Fausto
KeywordsMandelbrot set
Chaotic bands
Transformation rules
One-dimensional route
Nonlinear science
Issue Date13-Mar-2006
PublisherHindawi Publishing Corporation
CitationDiscrete Dynamics in Nature and Society 2006: 70471 (2006)
AbstractWe 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.
Description25 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
Appears in Collections:(IFA) Artículos
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