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tfg_cami_buzon_javier.pdf (662.59 KB)

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Bachelor thesis

Publication date

2022-06-13

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cc-by-nc-nd (c) Javier Camı́ Buzón, 2022
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/188821

Persistència de solucions quasi-periòdiques

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Abstract

[en] In this work, we study the persistence of invariant tori. Initially, we work on functional analysis in order to prove the mean value theorem and the inverse function theorem in Banach spaces, which will allow us to state and prove the implicit function theorem. Then, we apply those results to study a dynamical system which is perturbated by a quasi-periodic function in the neighborhood of an equilibrium point. During this analysis, we face the small divisors problem and we see the concept of the diophantine condition. Finally, we state and prove the Moser’s KAM theorem for twist maps.

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Àngel Jorba i Monte

Subject

Fluxos (Sistemes dinàmics diferenciables), Treballs de fi de grau, Espais de Banach, Sistemes hamiltonians

Subject (English)

Flows (Differentiable dynamical systems), Bachelor's theses, Banach spaces, Hamiltonian systems

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

CAMÍ BUZÓN, Javier. Persistència de solucions quasi-periòdiques. [consulted: 16 of June of 2026]. Available at: https://hdl.handle.net/2445/188821

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