%0 Generic %1 davis2020elastic %A Davis, Caroline %A Powell, Jasmine %A Winarski, Rebecca R. %A Yang, Jonguk %D 2020 %K complex_dynamics elastic_graphs thurston_maps %T Elastic Graphs for Main Molecule Matings %U http://arxiv.org/abs/2010.11382 %X 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.

@preprint{davis2020elastic, 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.}, added-at = {2020-10-23T17:45:46.000+0200}, author = {Davis, Caroline and Powell, Jasmine and Winarski, Rebecca R. and Yang, Jonguk}, biburl = {https://www.bibsonomy.org/bibtex/29c2fcac5e08e93d1f418cbc0831aed15/lukas.geyer}, description = {Elastic Graphs for Main Molecule Matings}, interhash = {b9a78400f1e86d52c31112eb20ef71e5}, intrahash = {9c2fcac5e08e93d1f418cbc0831aed15}, keywords = {complex_dynamics elastic_graphs thurston_maps}, note = {cite arxiv:2010.11382Comment: 21 pages, 5 figures}, timestamp = {2020-10-23T17:45:46.000+0200}, title = {Elastic Graphs for Main Molecule Matings}, url = {http://arxiv.org/abs/2010.11382}, year = 2020 }