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Title

Operating with external arguments in the Mandelbrot set antenna

AuthorsPastor, Gerardo; Romera, Miguel; Álvarez Marañón, Gonzalo; Montoya Vitini, Fausto
KeywordsMandelbrot set antenna
External arguments
External rays
Issue Date12-Jul-2002
PublisherElsevier
CitationPhysica D 171(1-2): 52-71 (2002)
AbstractThe external argument theory of Douady and Hubbard allows us to know both the potential and the field-lines in the exterior of the Mandelbrot set. Nonetheless, there are no explicit formulae to operate with external arguments, and the external argument theory is difficult to apply. In this paper we introduce some tools in order to obtain formulae to operate with external arguments in the Mandelbrot set antenna. Thus, we introduce the harmonic tool to calculate both the external arguments of the period-doubling cascade hyperbolic components and the external arguments of the last appearance hyperbolic components. Likewise, we introduce composition rules applied to external arguments that, with the aid of the concept of heredity, allows the calculation of all the external arguments that constitutes the family tree of a given external argument.
Description20 pages, 7 figures.-- PACS nrs.: 05.45.Ac; 47.20.Ky.-- Printed version published on Oct 2002.
Publisher version (URL)http://dx.doi.org/10.1016/S0167-2789(02)00539-0
URIhttp://hdl.handle.net/10261/8916
DOIhttp://dx.doi.org/10.1016/S0167-2789(02)00539-0
ISSN0167-2789
Appears in Collections:(IFA) Artículos
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