Julia Sets and Polynomial Roots

This lecture explores the generation and grouping of domains in the context of Julia Sets and polynomial roots. It delves into the application of Newton's method for finding roots, the complexity of solutions for equations of degree > 2, and the example of an immediate multiply connected domain. The lecture also discusses the critical points of functions, uniform convergence, and the splitting of the extended plane into regions converging to polynomial roots. Furthermore, it presents examples of polynomials and their roots, emphasizing the challenges posed by equations with degree > 2. The content concludes with insights into the convergence of roots and the behavior of functions around critical points.