Computer generated images for quadratic rational maps with a periodic critical point

Acta Mathematica Academiae Paedagogicae Nyíregyháziensis

Daniel Jackson¹  Dustin Gage¹ 

[1] University of Maine at Farmington

关键词: Mandelbrot set;   

DOI  :  

学科分类：数学（综合）

来源: Academia Paedagogica Nyiregyhaziensis. Acta Mathematica

【 摘 要 】

We describe an algorithm for distinguishing hyperbolic components in the parameter space of quadratic rational maps with a periodic critical point. We then illustrate computer images of the hyperbolic components of the parameter spaces $V_1-V_4$, which were produced using our algorithm. We also resolve the singularities of the projective closure of $V_5$ by blowups, giving an alternative proof that as an algebraic curve, the geometric genus of $V_5$ is 1. This explains why we are unable to produce an image for $V_5$.

【 授权许可】

Unknown