On the dynamics of generalized McMullen maps

Abstract

AbstractIn this paper, we study the dynamics of the two-parameter family of rational maps $$\begin{eqnarray*}{F}_{a, b} (z)= {z}^{n} + \frac{a}{{z}^{n} } + b.\end{eqnarray*}$$ We give the topological description of Julia sets and Fatou components of ${F}_{a, b} $ according to the dynamical behavior of the orbits of its free critical points.