EXISTENCE OF THE MANDELBROT SET IN PARAMETER PLANES FOR SOME GENERALIZED MCMULLEN MAPS

The paper proves the existence and multiplicity of baby Mandelbrot sets in parameter slices of R_{n,a,c}(z)=z^n+a/z^n+c by constructing explicit quadratic-like restrictions of R itself on wedge-shaped domains and invoking a standard parameter-winding criterion (its Theorem 2.3) together with Douady–Hubbard straightening. The candidate solution establishes the same conclusions via a different route: a root-lift semiconjugacy on an n-th root sector, parabolic anchors, and quadratic-like first return maps for a lifted degree-2 map. Parameter ranges and multiplicity statements match the paper’s theorems. Minor presentation gaps (e.g., analyticity of varying boundaries) are not substantive. Hence both are correct, with different proofs.