For the family of complex rational functions of the form \(R_{n,a,c}(z) = z^n + \dfrac{a}{z^n}+c\) , known as “Generalized McMullen maps”, for \(a\ne 0\) and \(n \ge 3\) fixed, we study the boundedness locus in some one-dimensional slices of the (a, c)-parameter space, by fixing a parameter or imposing a relation. First, if we fix c with \(|c|\ge 6\) while allowing a to vary, assuming a modest lower bound on n in terms of |c|, we establish the location in the a-plane of n “baby" Mandelbrot sets, that is, homeomorphic copies of the original Mandelbrot set. We use polynomial-like maps, introduced by Douady and Hubbard ([9]) and applied for the subfamily \(R_{n,a,0}\) by Devaney ([4]). Second, for slices in which \(c=ta\) , we again observe what look like baby Mandelbrot sets within these slices, and begin the study of this subfamily by establishing a neighborhood containing the boundedness locus.
