论文标题
合理功能的二次和立方牛顿地图
Quadratic and cubic Newton maps of rational functions
论文作者
论文摘要
完全描述了所有二次牛顿牛顿图的动力学。发现这样的地图的朱莉娅集是约旦曲线或完全断开的。事实证明，没有至少三个理性函数的牛顿地图与单次政治多项式（即，完全有一个有限的临界点）共轭。但是，有一些立方的牛顿地图与其他多项式共轭。这样的牛顿地图的朱莉娅集被证明是封闭曲线。每当牛顿地图有两个吸引人的固定点时，这都是乔丹曲线。
The dynamics of all quadratic Newton maps of rational functions are completely described. The Julia set of such a map is found to be either a Jordan curve or totally disconnected. It is proved that no Newton map with degree at least three of any rational function is conformally conjugate to a unicritical polynomial(i.e., with exactly one finite critical point). However, there are cubic Newton maps which are conformally conjugate to other polynomials. The Julia set of such a Newton map is shown to be a closed curve. It is a Jordan curve whenever the Newton map has two attracting fixed points.
