Julia Sets in Parameter Space for the Generalized McMullen Map

Mrs. Kelsey Brouwer
PhD Student
University of Wisconsin – Milwaukee

We will begin by introducing the field of complex dynamics and explaining the two types of pictures that dynamicists are interested in, namely Julia sets and parameter spaces. Next, we’ll introduce the generalized McMullen map and share some results about its Julia sets and parameter spaces. Finally, we will demonstrate an interesting connection between McMullen parameter space and quadratic Julia sets and discuss some potential techniques for explaining and documenting this phenomenon. A software demonstration may follow.