A combinatorial classification of postcritically fixed Newton maps
A combinatorial classification of postcritically fixed Newton maps
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DOI：
10.1017/etds.2018.2
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发表时间：
2007-01
影响因子：
0.9
通讯作者：
K. Drach;Yauhen Mikulich;Johannes Rückert;D. Schleicher
中科院分区：
文献类型：
--
作者：
K. Drach;Yauhen Mikulich;Johannes Rückert;D. Schleicher
对多项式动力系统的后临界不动牛顿映射类给出了一个组合分类。这为更一般的牛顿映射分类结果奠定了基础。一个基本要素是证明，对于每个牛顿映射（后临界有限或不），吸引不动点的盆的每个连通分量可以通过这样的分量的有限链连接到$\infty$。
We give a combinatorial classification for the class of postcritically fixed Newton maps of polynomials as dynamical systems. This lays the foundation for classification results of more general classes of Newton maps. A fundamental ingredient is the proof that for every Newton map (postcritically finite or not) every connected component of the basin of an attracting fixed point can be connected to $\infty$ through a finite chain of such components.