Suppose f and g are two post-critically finite polynomials of degree \(d_1\) and \(d_2\) respectively and suppose both of them have a finite super-attracting fixed point of degree \(d_0\). We prove that one can always construct a rational map R of degree

$$\begin{aligned} D = d_1 + d_2 - d_0 \end{aligned}$$

by gluing f and g along the Jordan curve boundaries of the immediate super-attracting basins. The result can be used to construct many rational maps with interesting dynamics.

中文翻译：

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对于多项式来说乔丹交配总是可能的

摘要

假设f和g分别是度为\(d_1\)和\(d_2\)的两个后临界有限多项式，并假设它们都具有度为\(d_0\)的有限超吸引不动点。我们证明，通过将f和g沿着直接超吸引的 Jordan 曲线边界粘合，总是可以构造一个度数为$$\begin{aligned} D = d_1 + d_2 - d_0 \end{aligned}$$的有理图R盆地。结果可以用来构建许多具有有趣动态的理性图。