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Algorithm for external argument calculation of the nodes of a shrub in the Mandelbrot set

AuthorsPastor, Gerardo; Romera, Miguel; Álvarez Marañón, Gonzalo; Arroyo Guardeño, David ; Orúe, Amalia B.; Fernández Mármol, Verónica ; Montoya Vitini, Fausto
KeywordsExternal arguments
Binary expansions
Mandelbrot set
Misiurewicz points
Nonlinear science
Issue DateJun-2008
PublisherWorld Scientific Publishing
CitationFractals 16(2): 159-168 (2008)
AbstractMisiurewicz points are essential points of the Mandelbrot set. External arguments are the most useful tool in order to analyze these points; therefore, it is important to go deeper in the study of the external arguments' calculation of these points. In this paper we introduce an algorithm to calculate the external arguments of the branch points, or nodes, of a shrub, since such nodes are the most outstanding Misiurewicz points of the chaotic region of the Mandelbrot set. Devaney and Moreno-Rocha had already presented a paper where they calculated the external arguments of one of these Misiurewicz points, the main node of a shrub. Our algorithm widens the study of Devaney and Moreno-Rocha because it allows one to calculate the external arguments of any node of the shrub.
Description10 pages, 4 figures.
Publisher version (URL)http://dx.doi.org/10.1142/S0218348X08003855
Appears in Collections:(IFA) Artículos
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