Dynamics of a family of quadratic maps in the quaternion space

被引：11

作者：

Nakane, S ^{[1
]}

机构：

[1] Tokyo Polytech Univ, Atsugi, Kanagawa 2430297, Japan

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2005年 / 15卷 / 08期

关键词：

quaternion; filled-in Julia set; Mandelbrot set; hyperbolic component; Green function;

D O I：

10.1142/S0218127405013460

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The dynamics of a family of quadratic maps in the quaternion space is investigated. In particular, connectivity of the filled-in Julia sets is completely determined. It is shown that the connectedness locus of this family is not equal to what we call the quaternionic Mandelbrot set. Hyperbolic components will also be completely characterized.

引用

页码：2535 / 2543

页数：9

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