论文标题
朱莉娅（Julia
The Julia sets of Chebyshev's method with small degrees
论文作者
论文摘要
给定多项式$ p $，确定其Chebyshev方法$ C_P $的程度。如果$ p $是立方体，则发现$ C_P $的度数为$ 4,6 $或$ 7 $，我们在这些情况下调查了$ C_P $的动态。如果立方多项式$ p $是单一政治或非传统的，则证明连接了$ C_P $的Julia集。作为Chebyshev的方法应用于非智力和通用的Cubyshev方法，所有有理图的家族都被其一个无关的固定点的乘数进行了参数。用乘以$C_λ$的乘数$λ$表示这个家庭的成员，我们已经表明，每当[-1,1] $中的$λ\时，$C_λ$的Julia套件都可以连接。
Given a polynomial $p$, the degree of its Chebyshev's method $C_p$ is determined. If $p$ is cubic then the degree of $C_p$ is found to be $4,6$ or $7$ and we investigate the dynamics of $C_p$ in these cases. If a cubic polynomial $p$ is unicritical or non-generic then, it is proved that the Julia set of $C_p$ is connected. The family of all rational maps arising as the Chebyshev's method applied to a cubic polynomial which is non-unicritical and generic is parametrized by the multiplier of one of its extraneous fixed points. Denoting a member of this family with an extraneous fixed point with multiplier $λ$ by $C_λ$, we have shown that the Julia set of $C_λ$ is connected whenever $λ\in [-1,1]$.
