Chebyshev-Halley家族在n次多项式上的Julia集连通性
Connectivity of the Julia set for the Chebyshev-Halley family on degree n polynomials
AI总结：
研究Chebyshev-Halley根寻找算法的复动力学特性，发现吸引盆地非单连通时收敛速度减慢，提出保证吸引盆地单连通性的准则，并分析n次多项式z^n+c参数对Julia集连通性的影响。
摘要：
我们从复动力学角度研究Chebyshev-Halley根寻找算法族。数值实验表明，当吸引盆地不单连通时，收敛速度可能变慢。本文提供了一个保证根的吸引盆地单连通性的准则。我们利用该准则研究Chebyshev-Halley方法应用于n次多项式z^n+c的情况，获得所有Fatou分量单连通的参数特征，从而确定Julia集连通性。我们还研究了增加n对动力学的影响。
英文摘要：
We study the Chebyshev-Halley family of root finding algorithms from the point of view of holomorphic dynamics. Numerical experiments show that the speed of convergence to the roots may be slower when the basins of attraction are not simply connected. In this paper we provide a criterion which guarantees the simple connectivity of the basins of attraction of the roots. We use the criterion for the Chebyshev-Halley methods applied to the degree $n$ polynomials $z^n+c$, obtaining a characterization of the parameters for which all Fatou components are simply connected and, therefore, the Julia set is connected. We also study how increasing $n$ affects the dynamics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
