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Title

Shrubs in the Mandelbrot set ordering

AuthorsRomera, Miguel; Pastor, Gerardo; Álvarez Marañón, Gonzalo; Montoya Vitini, Fausto
KeywordsMandelbrot set
Hyperbolic components
Misiurewicz points
Issue Date2003
PublisherWorld Scientific Publishing
CitationInt. J. Bifurcation and Chaos 13(8): 2279-2300 (2003)
AbstractWe introduce shrubs in this paper in order to present a first approach to studying the structure of the Mandelbrot set. Primary, secondary... and N-ary shrubs are analyzed. We have experimentally obtained formulae to calculate the periods of the hyperbolic component representatives of the structural branches, and the preperiods and periods of both the nodes -where structural branches emanate- and the tips -where the shrub enters in crisis. A generalization allows us to give in each case one formula to calculate representative periods and preperiods and periods of nodes and tips.
Description22 pages, 9 figures.
Publisher version (URL)http://dx.doi.org/10.1142/S0218127403007941
URIhttp://hdl.handle.net/10261/8914
DOIhttp://dx.doi.org/10.1142/S0218127403007941
ISSN0218-1274
Appears in Collections:(IFA) Artículos
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