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On periodic and chaotic regions in the Mandelbrot set

AuthorsPastor, Gerardo; Romera, Miguel; Álvarez Marañón, Gonzalo; Arroyo Guardeño, David ; Montoya Vitini, Fausto
KeywordsMandelbrot set
Chaotic regions
Periodic regions
Nonlinear science
Issue DateApr-2007
CitationChaos, Solitons & Fractals 32(1): 15-25 (2007)
AbstractWe show here in a graphic and simple way the relation between the periodic and chaotic regions in the Mandelbrot set. Since the relation between the periodic and chaotic regions in a one-dimensional (1D) quadratic set is already well known, we shall base on it to extend the results to the Mandelbrot set. We shall see that in the same way as the hyperbolic components of the period-doubling cascade determines the chaotic bands structure in 1D quadratic sets, the periodic region determines the chaotic region in the Mandelbrot set.
Description11 pages, 5 figures.-- Available online Dec 20, 2005.
Publisher version (URL)http://dx.doi.org/10.1016/j.chaos.2005.10.099
Appears in Collections:(IFA) Artículos
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