Abstract:

We consider the family of rational maps given by $F_λ(z) = z^n+λ/z^d$

where $n,d ∈ mathbb N$ with $1/n+1/d < 1$, the variable $z in mathbb  C$ and the pa-

rameter $λ in mathbb  C$. It is known that when $n = d ≥ 3$ there are infinitely

many rings $S_k$ with $k in mathbb N$, around the McMullen domain.

We generalize the existence of these rings to the case

when $1/n+1/d < 1$ where $n$ is not necessarily equal to $d$.

This is a joint work with HyeGyong Jang and Sebastian Marotta.