An effective algorithm to compute Mandelbrot sets in parameter planes

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 effect...

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Detalles Bibliográficos
Autores: Garijo, Antoni|||0000-0002-1503-7514, Jarque i Ribera, Xavier|||0000-0002-6576-9780, Villadelprat Yagüe, Jordi|||0000-0002-1168-9750
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:182522
Acceso en línea:https://ddd.uab.cat/record/182522
https://dx.doi.org/urn:doi:10.1007/s11075-017-0270-8
Access Level:acceso abierto
Palabra clave:Algorithm
Bifurcation locus
Holomorphic dynamics
Julia and Fatou sets
Mandelbrot set
Misiurewicz bifurcation
Descripción
Sumario: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.