$n$次Chebyshev-Halley多项式族中的类牛顿分支
Newton-like components in the Chebyshev-Halley family of degree $n$ polynomials
摘要：
本文研究了多项式族$f_{n,c}(z)=z^n+c$的Cebyshev-Halley方法，分别用于$n\ge 2$和$c\in \mathbb{C}^{*}$ .我们证明了参数的存在，使立即盆地的吸引力对应的根的单位是无限连接的。我们还证明了，$n \ge 2$，相应的动力平面包含一个连通分支的朱利亚集，这是一个拟共形变形的朱利亚集的映射通过应用牛顿法$f_{n,-1}$。
英文摘要：
We study the Cebyshev-Halley methods applied to the family of polynomials $f_{n,c}(z)=z^n+c$, for $n\ge 2$ and $c\in \mathbb{C}^{*}$. We prove the existence of parameters such that the immediate basins of attraction corresponding to the roots of unity are infinitely connected. We also prove that, for $n \ge 2$, the corresponding dynamical plane contains a connected component of the Julia set, which is a quasiconformal deformation of the Julia set of the map obtained by applying Newton's method to $f_{n,-1}$.
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