On Newton's method for entire functions
On Newton's method for entire functions
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DOI：
10.1112/jlms/jdm046
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发表时间：
2005-05
期刊：
影响因子：
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通讯作者：
Johannes Rueckert;D. Schleicher
中科院分区：
文献类型：
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作者：
Johannes Rueckert;D. Schleicher
整个函数f的牛顿映射Nf把f的根变成吸引不动的点。设U为Nf这样一个不动点的直接吸引盆。我们研究了Nf在U的分量V中的行为。如果V可以被U内的不变曲线所包围，并且满足对于所有z∈，Nf−1({z})∩V是有限集的条件，则证明V包含Nf的另一个直接盆或虚直接盆。
The Newton map Nf of an entire function f turns the roots of f into attracting fixed points. Let U be the immediate attracting basin for such a fixed point of Nf. We study the behavior of Nf in a component V of ℂ\U. If V can be surrounded by an invariant curve within U and satisfies the condition that for all z ∈ ℂ̂, Nf−1({z}) ∩ V is a finite set, then it is shown that V contains another immediate basin of Nf or a virtual immediate basin.