Elastic Graphs for Main Molecule Matings
Dynamical Systems
2020-10-23 v1
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.
Keywords
Cite
@article{arxiv.2010.11382,
title = {Elastic Graphs for Main Molecule Matings},
author = {Caroline Davis and Jasmine Powell and Rebecca R. Winarski and Jonguk Yang},
journal= {arXiv preprint arXiv:2010.11382},
year = {2020}
}
Comments
21 pages, 5 figures