论文标题
具有固定临界点的立方多项式的底漆。第二部分：$α$ - 四肢对称
Matings of cubic polynomials with a fixed critical point. Part II: $α$-symmetry of limbs
论文作者
论文摘要
在本文中，我们为两个在$ \ mathcal {s} _1 $中的两种后有限多项式的交配提供了足够（构想，必要的）条件（称为$α$ - 符号对称）。为此，我们研究了与$ \ Mathcal {s} _1 $的连接度座位中与参数四肢相关的旋转集，这使我们能够确定何时在包含封闭环的正式交配中存在射线类。我们提供证明$α$ -Symmetry的必要性，以$ \ MATHCAL {S} _1 $的特定子集的特定后集有限的图。给出了许多示例以说明本文的结果。
In this article we provide a combinatorial sufficient (and conjecturally, necessary) condition (called $α$-symmetry) for the mating of two postcritically finite polynomials in $\mathcal{S}_1$ to be obstructed. To do this, we study the rotation sets associated to the parameter limbs in the connectedness locus of $\mathcal{S}_1$, which allows us to determine when there exist ray classes in the formal mating which contain a closed loop. We give a proof of the necessity of $α$-symmetry for a particular subset of postcritically finite maps in $\mathcal{S}_1$. Many examples are given to illustrate the results of the paper.
