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Jordan mating is always possible for polynomials

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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

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

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.

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Acknowledgements

I would like to thank Fei Yang who provides all the computer generating pictures in the paper. Besides this, I am very grateful to the anonymous referee for his detailed comments and suggestions which greatly improved the early version of the manuscript. The work is partially supported by NSFC(grant NO. 12171276).

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  1. Department of Mathematics, QuFu Normal University, Qufu, 273165, People’s Republic of China

    Gaofei Zhang

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  1. Gaofei Zhang
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Correspondence to Gaofei Zhang.

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Zhang, G. Jordan mating is always possible for polynomials. Math. Z. 306, 71 (2024). https://doi.org/10.1007/s00209-024-03465-0

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