# name
Teoria del grau, teorema de Schauder i aplicacions

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Ernest Fontich

# metadata.dc.description.abstract[].value
[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.

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cc-by-nc-nd (c) Marc Peradalta Negre, 2022

# metadata.dc.source[].value
Treballs Finals de Grau (TFG) - Matemàtiques

# metadata.dc.title[].value
Teoria del grau, teorema de Schauder i aplicacions