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http://hdl.handle.net/2445/186761
Title: | Teoria del grau, teorema de Schauder i aplicacions |
Author: | Peradalta Negre, Marc |
Director/Tutor: | Fontich, Ernest, 1955- |
Keywords: | Sistemes dinàmics de baixa dimensió Treballs de fi de grau Teoria del punt fix Varietats (Matemàtica) Operadors no lineals Low-dimensional dynamical systems Bachelor's theses Fixed point theory Manifolds (Mathematics) Nonlinear operators |
Issue Date: | 24-Jan-2022 |
Abstract: | [en] The aim of this project is to introduce degree theory and its applications. We analyse the degree for functions defined over finite-dimensional and infinite-dimensional normed spaces, together with its main properties. One of these properties allows us to connect degree theory with fixed-point theory. As a result, we demonstrate some fundamental fixed-point theorems, like Brouwer’s theorem or its generalisation to infinite-dimensional spaces, Schauder’s theorem. The latter is applied in two instances. Firstly, we prove the existence of one-dimensional invariant manifolds for a certain class of planar maps. Secondly, we demonstrate the existence of periodic solutions for the forced pendulum equation. |
Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Ernest Fontich |
URI: | http://hdl.handle.net/2445/186761 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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tfg_peradalta_negre_marc.pdf | Memòria | 757.52 kB | Adobe PDF | View/Open |
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