Mating Critically Infinite And Quasi-starlike Quadratic Polynomials

In this paper, we prove the existence and uniqueness of matingsof f(-7/8) = z~2 - 7/8, which is not critically finite and has a periodic point withperiod 2, with any quadratic polynomial which lies outside of the 1/2-limb of M,is nonrenormalizable, and does not have any non-repelling periodic orbits. Theapproach consists of constructing a Yoccoz puzzle partition by bubble rays whichin place of external rays, based on M. Aspenberg and M. Yampolsky's idea.