阳卫锋.一类整函数的牛顿法的拟直接盘和直接盘[J].数学研究及应用,2010,30(5):920~928 |
一类整函数的牛顿法的拟直接盘和直接盘 |
Virtual and Immediate Basins of Newton's Method for a Class of Entire Functions |
投稿时间:2008-06-10 修订日期:2010-01-19 |
DOI:10.3770/j.issn:1000-341X.2010.05.021 |
中文关键词: 牛顿法 Baker域 拟直接盘 Fatou集 Julia集. |
英文关键词:Newton's method Baker domain virtual immediate Basin Fatou set Julia set. |
基金项目:湖南省教育厅资助科研项目 (Grant No.06C245). |
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中文摘要: |
本文讨论一类无穷阶亚纯函数的牛顿迭代法.利用在一个完全不连通的紧集之外亚纯的函数的动力学理论,发现牛顿迭代系统的Fatou集中有多列拟直接盘,在其中牛顿迭代趋于无穷远;同时有一列面积有限的直接盘. |
英文摘要: |
In this paper, we consider Newton's method for a class of entire functions with infinite order. By using theory of dynamics of functions meromorphic outside a small set, we find there are some series of virtual immediate basins in which the dynamics converges to infinity and a series of immediate basins with finite area in the Fatou sets of Newton's method. |
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