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arXiv · 2208.10069

Jordan mating is always possible for polynomials

Gaofei Zhang
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Abstract

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 $$D = d_1 + d_2 - d_0$$ 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.

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Gaofei Zhang. 2022-08-22. Jordan mating is always possible for polynomials. https://arxiv.org/abs/2208.10069

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