Jordan mating is always possible for polynomials

期刊论文
发表日期：

2024年3月15日

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Gaofei Zhang

摘要

Suppose f and g are two post-critically finite polynomials of degree $d_1$ $d_{1}$ and $d_2$ $d_{2}$ respectively and suppose both of them have a finite super-attracting fixed point of degree $d_0$ $d_{0}$ . We prove that one can always construct a rational map R of degree $\begin{aligned} D = d_1 + d_2 - d_0 \end{aligned}$ $\begin{matrix} D = d_{1} + d_{2} - d_{0} \end{matrix}$ 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.