Renormalization in complex dynamics

Abstract

[en] Renormalization theory is a powerful technique both in mathematics and physics. In particular, it is essential in the study of the MLC conjecture, which wonders whether or not the Mandelbrot set is locally connected. The main purpose of this project is to comprehend the Straightening Theorem with the utmost rigour, that is an essential result behind the aforementioned technique. In order to approach our aim, we proceed to concentrate on quasiconformal geometry and give some basic background concerning dynamical systems. Besides, we explore some applications of the cornerstone of this thesis within the framework of complex dynamics. Lastly, we outline the notion of renormalization when dealing with percolation theory in physics.