An effective algorithm to compute Mandelbrot sets in parameter planes

被引：2

作者：

Garijo, Antonio ^{[1
]}

Jarque, Xavier ^{[2
,3
]}

Villadelprat, Jordi ^{[1
]}

机构：

[1] Univ Rovira & Virgili, Dept Engn Informat & Matemat, E-43007 Tarragona, Catalonia, Spain

[2] Univ Barcelona, Dept Matemat & Informat, E-08007 Barcelona, Catalonia, Spain

[3] Univ Barcelona, Grad Sch Math, E-08007 Barcelona, Catalonia, Spain

来源：

NUMERICAL ALGORITHMS | 2017年 / 76卷 / 02期

关键词：

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

D O I：

10.1007/s11075-017-0270-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：555 / 571

页数：17

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