Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/122304
Title: Siegel's linearization theorem
Author: Raich Bros, Carles
Director/Tutor: Haro, Àlex
Keywords: Aplicacions holomòrfiques
Treballs de fi de grau
Sistemes dinàmics diferenciables
Equació de Schrödinger
Corbes algebraiques
Holomorphic mappings
Bachelor's thesis
Differentiable dynamical systems
Schrödinger equation
Algebraic curves
Issue Date: 7-Jul-2017
Abstract: [en] The purpose of this study is to give an insight to Siegel’s linearization theorem, a result in discrete dynamics of one-dimensional holomorphic maps that claims the existence of a change of coordinates in a neighbourhood of a map’s fixed point to its linear part, whenever the multiplier for such point satisfies the Diophantine condition. This overall approach aims to provide an understanding of the theorem and all it encompasses. It firstly puts forward necessary knowledge in Diophantine approximations as well as complex and functional analysis and introduces some background to Schröder’s equation, the conjugacy problem in which the theorem originates. Once set, the theorem is proved in great detail and the dissertation concludes with a numerical exploration performed to visualize and ponder about the most relevant results forementioned.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Àlex Haro
URI: http://hdl.handle.net/2445/122304
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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