Important properties pertaining to families of discrete dynamical systems are furnished here by studying the kneading theory developed by Milnor and Thurston, and subsequently implementing the spider algorithm, developed by Hubbard and Schleicher. The focus is on identifying crucial combinatorial and numerical properties of periodic critical orbits in one-dimensional discrete dynamical systems, which are generated … Continue reading A Mathematica Implementation of Nonlinear Dynamical Systems Theory via the Spider Algorithm and Finding Critical Zeros of High-Degree Polynomials