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Title: Quasi-periodic solutions in quasi-periodic systems via Fourier transforms
Author: Sandín Vidal, Eric
Director: Haro, Àlex
Keywords: Sistemes dinàmics diferenciables
Treballs de fi de grau
Sistemes dinàmics hiperbòlics
Transformacions de Fourier
Anàlisi numèrica
Differentiable dynamical systems
Bachelor's thesis
Hyperbolic dynamical systems
Fourier transformations
Numerical analysis
Issue Date: 27-Jun-2018
Abstract: [eng] Within the field of dynamical systems, one shall find a special sort of systems, systems that revolve around external perturbations, either periodic or quasi-periodic, the so called skew-product dynamical systems. Even though the study of these systems can be a very helpful source of tools for an engineering or more practical work that may present systems alike, the main focus of this project is of a more theoretical nature. What is about to be presented is an approach to response solutions of such perturbated systems and the proof of existence and uniqueness of invariant fiberwise hyperbolic tori given an approximate torus of such characteristics, and the further expression of the proof’s conditions in computable terms via Fourier transforms. Besides the theoretical part, it is also provided an algorithm and its respective computational implementation that allows to simplify the expression of the linear dynamics of a system under a quasi-periodic perturbation into a diagonal matrix at the cost of an error that will significantly decrease at each step of the algorithm.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Àlex Haro
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques
Programari - Treballs de l'alumnat

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