Exploring parameter spaces in complex dynamics

Abstract

We show the structure of the parameter space for a family of rational maps containing Blaschke products. Through numerical simulations using the orbit of a single critical point, we reveal the existence of infinitely many Mandelbrot-like sets along the unit circle, as well as eight-like structures in other regions of parameter space. We pose some open questions related to the parameter space of these functions.

Keywords

• complex dynamics
• blaschke products
• mandelbrot set
• julia set