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arXiv · 2010.11382

Elastic Graphs for Main Molecule Matings

Caroline Davis·Jasmine Powell·Rebecca R. Winarski·Jonguk Yang
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Abstract

Recent work of Dylan Thurston gives a condition for when a post-critically finite branched self-cover of the sphere is equivalent to a rational map. We apply D. Thurston's positive criterion for rationality to give a new proof of a theorem of Rees, Shishikura, and Tan about the mateability of quadratic polynomials when one polynomial is in the main molecule. These methods may be a step in understanding the mateability of higher degree post-critically finite polynomials and demonstrate how to apply the positive criterion to classical problems.

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Caroline Davis, Jasmine Powell, Rebecca R. Winarski, Jonguk Yang. 2020-10-22. Elastic Graphs for Main Molecule Matings. https://arxiv.org/abs/2010.11382

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