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memoria.pdf (3.16 MB)

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Bachelor thesis

Publication date

2018-06-27

Publication license

cc-by-nc-nd (c) Abel Hernández Ruiz, 2018
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/127335

Renormalization in complex dynamics

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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.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Núria Fagella Rabionet

Subject

Sistemes dinàmics complexos, Treballs de fi de grau, Teoria geomètrica de funcions, Funcions enteres, Funcions meromorfes, Mecànica estadística

Subject (English)

Complex dynamical systems, Bachelor's theses, Geometric function theory, Entire functions, Meromorphic functions, Statistical mechanics

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

HERNÁNDEZ RUIZ, Abel. Renormalization in complex dynamics. [consulted: 7 of August of 2026]. Available at: https://hdl.handle.net/2445/127335

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