Structure of the McMullen domain in the parameter planes for rational maps

We show that, for the family of functions F-lambda (z) = z(n) + lambda/z(n) where n >= 3 and lambda is an element of C, there is a unique McMullen domain in parameter space. A McMullen domain is a region where the Julia set of F-lambda is homeomorphic to a Cantor set of circles. We also prove that this McMullen domain is a simply connected region in the plane that is bounded by a simple closed curve.