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Pàgina inicial > Articles > Articles publicats > An effective algorithm to compute Mandelbrot sets in parameter planes |
Data: | 2017 |
Resum: | 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. |
Ajuts: | Ministerio de Economía y Competitividad MTM2014-52209-C2-1-P Ministerio de Economía y Competitividad MTM2014-52209-C2-2-P |
Nota: | 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. |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Algorithm ; Bifurcation locus ; Holomorphic dynamics ; Julia and Fatou sets ; Mandelbrot set ; Misiurewicz bifurcation |
Publicat a: | Numerical Algorithms, Vol. 76 (2017) , p. 555-571, ISSN 1572-9265 |
Postprint 15 p, 3.0 MB |