Last time, we found a parametrization for the family \(Per_1(1)\) of conjugacy classes of rational maps of degree 2 with a fixed point with multiplier 1, and we defined the Parabolic Mandelbrot Set \(M_1\) to be the connectedness locus of this family.

This time, we will talk about the Parabolic Flower Theorem to describe the dynamics at the parabolic fixed point \(P\), and we will sketch a proof to the fact given last time: the Julia set is disconnected if and only if both critical points belong to the same immediate basin of attraction adjacent to \(P\).