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...
| Autores: | , , |
|---|---|
| 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 |
| 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. |
|---|