Shared matings in $V_2$

Abstract

We give a new constructive method to prove existence of shared matings in the special class $V_2$ consisting of rational maps with a super-attracting $2$-cycle (up to M\"obius conjugacy). The proof does not use Thurston's Theorem on branched coverings on the Riemann sphere. The background to this paper is the master thesis of L. Pedersen (Ume\r{a} University, 2014), where one special shared mating was studied.