Conley-Morse databases for the angular dynamics of Newton's method on the plane

In this paper we showcase the technique of Conley-Morse databases for studying a parameterized family of dynamical systems. The dynamical system of interest arises from considering the limiting behavior of Newton's root-finding method applied to functions f: ℝ² → ℝ² when the iterates converge to the origin. Considering the progression of angular orientations gives rise to a selfmap of the unit circle we call the angular dynamics map. We demonstrate how the technique of Conley-Morse dynamical databases allows us to quickly survey and prove theorems about the global dynamics of the parameterized family of angular dynamics maps.