论文标题
Chebyshev-Halley的学位$ n $多项式的类似牛顿的组件
Newton-like components in the Chebyshev-Halley family of degree $n$ polynomials
论文作者
论文摘要
我们研究了适用于多项式家庭的cebyshev-halley方法$ f_ {n，c}（z）= z^n+c $，对于$ n \ ge 2 $和$ c \ in \ in \ mathbb {c}^{*} $。我们证明了参数的存在，因此与统一根相对应的吸引力的直接盆地是无限连接的。我们还证明，对于$ n \ ge 2 $，相应的动态平面包含朱莉娅集合的连接组件，这是通过将牛顿的方法应用于$ f_ {n，-1} $获得的地图的朱莉娅集合的准形式变形。
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 $f_{n,-1}$.
