Fatou Components and Julia Sets of Singularly Perturbed Rational Maps with Positive Parameter

• Published in: Acta mathematica Sinica. English series Vol. 28; no. 10; pp. 1937 - 1954
• Main Authors: Qiu, Wei Yuan, Xie, Lan, Yin, Yong Cheng
• Format: Journal Article
• Language: English
• Published: Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.10.2012; Springer Nature B.V
• Subjects: Basins; Boundaries; Cantor集; Fatou分支; Julia集; Mathematical analysis; Mathematics; Mathematics and Statistics; Orbits; Studies; Zinc; 参数摄动; 吸引盆; 固定点; 地图; 抛物线; Jordan domain; local connectivity; 37F10; Sierpiński curve; Julia set; Fatou component

In this paper, we discuss the rational maps Fλ（z）=z^n＋λ/z^n,n≥2with the positive real parameter ）λ. It is shown that the immediately attracting basin Bλ of ∞ for Fλ is always a Jordan domain if the Julia set of Fλ is not a Cantor set. Fuhermore, Bλ is a quasidisk if there is no parabolic fixed point...