An effective algorithm to compute Mandelbrot sets in parameter planes

作者：Garijo Antonio; Jarque Xavier^*; Villadelprat Jordi

来源：Numerical Algorithms, 2017, 76(2): 555-571.

DOI：10.1007/s11075-017-0270-8

• Holomorphic dynamics
• Julia and Fatou sets
• Bifurcation locus
• Misiurewicz bifurcation
• Mandelbrot set
• Algorithm

In McMullen (2000) it was proven 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.

• 出版日期2017-10