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Title: Renormalization in complex dynamics
Author: Hernández Ruiz, Abel
Director/Tutor: Fagella Rabionet, Núria
Keywords: Sistemes dinàmics complexos
Treballs de fi de grau
Teoria geomètrica de funcions
Funcions enteres
Funcions meromorfes
Mecànica estadística
Complex dynamical systems
Bachelor's thesis
Geometric function theory
Entire functions
Meromorphic functions
Statistical mechanics
Issue Date: 27-Jun-2018
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.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Núria Fagella Rabionet
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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