论文标题
在具有抛物线固定点的立方多项式的动态参数空间上
On Dynamical Parameter Space of Cubic Polynomials with a Parabolic Fixed Point
论文作者
论文摘要
本文重点介绍了Cubic多项式切片$ per_1（λ）$的连接基因座，其抛物线固定点$λ= e^{2πi\ frac {p} {q} {q}}} $。我们首先表明，任何是双曲线分量的平行概念的任何抛物线分量都是Jordan域。此外，定义了连接基因座中的中心部分的连续$ \ MATHCAL {K}_λ$。这是闭合$ per_1（0）$的主要双曲部件的自然类似物。我们证明，$ \ MATHCAL {K}_λ$几乎是对二次多项式$p_λ（z）=λz+z^2 $的填充朱莉亚集的双重覆盖。
This article focus on the connected locus of the cubic polynomial slice $Per_1(λ)$ with a parabolic fixed point of multiplier $λ=e^{2πi\frac{p}{q}}$. We first show that any parabolic component, which is a parallel notion of hyperbolic component, is a Jordan domain. Moreover, a continuum $\mathcal{K}_λ$ called the central part in the connected locus is defined. This is the natural analogue to the closure of the main hyperbolic component of $Per_1(0)$. We prove that $\mathcal{K}_λ$ is almost a double covering of the filled-in Julia set of the quadratic polynomial $P_λ(z) = λz+z^2$.
