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Algorithm for external arguments calculation of the nodes of a shrub in the Mandelbrot set. (English) Zbl 1163.37012

R. L. Devaney and M. Moreno Rocha [Fractals 10, No. 1, 39–46 (2002; Zbl 1072.37506)] calculated, mathematically, the external arguments of Douady and Hubbard of the main node of a shrub of the Mandelbrot set, using two different approaches: one for the first and last external arguments and another one for the intermediate arguments. In the present paper, the authors develop a single computational algorithm capable of calculating all external arguments not only of the main node of a shrub, but also of the infinite number of nodes of a shrub of the Mandelbrot set. Numerial and illustrative examples are presented.

MSC:

37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations (MSC2010)

Citations:

Zbl 1072.37506
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References:

[1] DOI: 10.1142/S0218348X02000926 · Zbl 1072.37506
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