Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Wandering around the Mandelbrot set

Talk by Prof. Dr. Mikhael Lyubich

**Date:** 27.09.21 **Time:** 15.00 - 16.00 **Room:** Y27H28

The Mandelbrot set M encodes in one picture the whole dynamical story of the complex quadratic family f_c(z)= z^2+c. This story is quite remarkable, beginning with a simple map z^2 and then developing, through a sequence of bifurcations, intricate chaotic and fractal structures. In some places it is self-similar, while in others is completely unrecognizable. How to make sense of these patterns? There are powerful geometric and dynamical ideas that lead to a comprehensive understanding of the set. But there is also one open problem on the way: ``MLC Conjecture" asserting that M is locally connected.