Bifurcation and fractals in complex dynamical systems

This lecture by the instructor explores the concepts of bifurcation and fractals in complex dynamical systems, focusing on the iteration of holomorphic maps on complex manifolds. It delves into the behavior of polynomial maps on the complex plane, discussing various Julia sets, including disconnected and totally disconnected sets. The lecture also covers the Mandelbrot set and the color scheme used to represent different sets. Additionally, it discusses the self-similarity of Julia sets induced by the dynamics themselves, the theory of renormalization, and the distinction between renormalizable and non-renormalizable systems.