Quid of Complex Fractals and their Combinatorics
par
207
Salle Pellos
"The classic question of complex dynamics is what happens when we iterate a complex analytical function. Even very simple maps can produce remarkably complicated behavior, giving rise to fractal sets with rich geometric and combinatorial structures. One of the most known examples comes from the quadratic family z^2+c, whose dynamics give rise to the famous Mandelbrot set.
In this talk, I will give an introduction to the Julia Sets and the Mandelbrot Set, and present a combinatorial framework for analyzing their structure. Several combinatorial frameworks like this have been developed in the literature for studying the quadratic family. Here, we focus on a framework introduced by Pascale Roesch and Carsten Petersen, which provides an important tool for comparing the classical setting with its parabolic counterpart, the so-called Parabolic Mandelbrot set."