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2017-01-01

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/124910

An effective algorithm to compute Mandelbrot sets in parameter planes.

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https://doi.org/10.1007/s11075-017-0270-8

Abstract

McMullen in 2000 proved that copies of generalized Mandelbrot set are dense in the bifurcation locus for generic families of rational maps. We develop an algorithm to an effective computation of the location and size of these generalized Mandelbrot sets in parameter space. We illustrate the effectiveness of the algorithm by applying it to concrete families of rational and entire maps.

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Sistemes dinàmics complexos, Teoria de la mesura, Equacions funcionals, Desigualtats (Matemàtica)

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Complex dynamical systems, Measure theory, Functional equations, Inequalities (Mathematics)

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GARIJO REAL, Antonio, JARQUE I RIBERA, Xavier and VILLADELPRAT, Jordi. An effective algorithm to compute Mandelbrot sets in parameter planes. Numerical Algorithms. 2017. Vol. 76, num. 2, pags. 555-571. ISSN 1017-1398. [consulted: 6 of June of 2026]. Available at: https://hdl.handle.net/2445/124910

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