External arguments for the chaotic bands calculation in the Mandelbrot set
نویسندگان
چکیده
منابع مشابه
External arguments for the chaotic bands calculation in the Mandelbrot set
In this paper we study the chaotic bands of any Mandelbrot set hyperbolic component. We use external arguments in order to identify the hyperbolic components. If we use harmonics as a tool, we can calculate the chaotic bands. Indeed, as we clearly show here, the harmonics of the external arguments of a given hyperbolic component (gene) are the external arguments of the last appearance hyperboli...
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Hyperbolic components and Misiurewicz points of the chaotic region of the Mandelbrot set are located in what we call shrubs. Each shrub has two well-differentiated parts. The first one, shrub0; corresponds to the main branch of the shrub. The second one, shrubr; corresponds to all the other branches of the shrub. In this paper, we have focused on the ordering of the hyperbolic components and Mi...
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We 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...
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Near to the cusp of a cardioid of the Mandelbrot set, except for the main cardioid, there is a sequence of baby Mandelbrot sets. Each baby Mandelbrot set is in the center of a Douady cauliflower, a decoration constituted by an infinity of minute Mandelbrot sets and Misiurewicz points linked by filaments. A Douady cauliflower appears to have a complicated structure, and how the external rays lan...
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The 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 Mandel...
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ژورنال
عنوان ژورنال: Physica A: Statistical Mechanics and its Applications
سال: 2005
ISSN: 0378-4371
DOI: 10.1016/j.physa.2005.02.025