An effective algorithm to compute Mandelbrot sets in parameter planes
Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)

Date:	2017
Abstract:	In 2000 McMullen proved that copies of generalized Mandelbrot set are dense in the bifurcation locus for generic families of rational maps. We develop an algo- rithm 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.
Grants:	Ministerio de Economía y Competitividad MTM2014-52209-C2-1-P Ministerio de Economía y Competitividad MTM2014-52209-C2-2-P
Note:	Agraïments: The second author is partially supported by the Polish NCN grant decision DEC-2012/06/M/ST1/00168 and the MDM-2014-445 Maria de Maeztu.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Algorithm ; Bifurcation locus ; Holomorphic dynamics ; Julia and Fatou sets ; Mandelbrot set ; Misiurewicz bifurcation
Published in:	Numerical Algorithms, Vol. 76 (2017) , p. 555-571, ISSN 1572-9265

DOI: 10.1007/s11075-017-0270-8

Postprint 15 p, 3.0 MB

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