Super-attracting cycles for the cosine-root family

We investigate the dynamics of the cosine-root family, Cλ(z)=λcosz, where λ∈Cλ∈C. When λ∈Rλ∈R, we focus on the distribution of super-attracting cycles associated to the two critical values. In particular, we locate the parameters leading to super-attracting three cycles for one of the critical values while the other critical value is attracted to a fixed point. These results are used to verify observations made upon viewing Julia and parameter plane pictures.