Amb motiu del tancament d'estiu, la validació de documents es reprendrà a partir del 28 d'agost de 2026. Disculpeu les molèsties.
Con motivo del cierre de verano, la validación de documentos se reanudará a partir del 28 de agosto de 2026. Disculpad las molestias
Due to the summer closure, document validation will resume starting August 28, 2026. We apologize for any inconvenience.

Files

memoria.pdf (4.14 MB)
redu-fft.c (19.16 KB)

Document type

Bachelor thesis

Publication date

2018-06-27

Publication license

cc-by-nc-nd (c) Eric Sandín Vidal, 2018
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/127600

Quasi-periodic solutions in quasi-periodic systems via Fourier transforms

Journal Title

Authors

Director/Tutor

Journal ISSN

Volume Title

Related resource

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.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Àlex Haro

Subject

Sistemes dinàmics diferenciables, Treballs de fi de grau, Sistemes dinàmics hiperbòlics, Transformacions de Fourier, Anàlisi numèrica

Subject (English)

Differentiable dynamical systems, Bachelor's theses, Hyperbolic dynamical systems, Fourier transformations, Numerical analysis

Citation

Collections

Treballs Finals de Grau (TFG) - Matemàtiques
Programari - Treballs de l'alumnat

Citation

SANDÍN VIDAL, Eric. Quasi-periodic solutions in quasi-periodic systems via Fourier transforms. [consulted: 11 of August of 2026]. Available at: https://hdl.handle.net/2445/127600

Export metadata

JSON - METS

Share record