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memoria.pdf (485.04 KB)

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Bachelor thesis

Publication date

2018-06-27

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cc-by-nc-nd (c) Elies M. Gil Fuster, 2018
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/126669

Completely integrable systems on hamiltonian mechanics

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Abstract

[en] During the last two centuries, the study of mechanics has enjoyed a remarkable evolution, in parallel with one of its main mathematical tools: symplectic geometry. In this text, some of the most important notions have been gathered for the understanding of the Liouville-Arnold Theorem on completely integrable systems. The final goal of this project is to give a new approach to this fundamental result; thus the theory presented is appropriately nourished with humble examples to be analyzed. During the work previous to the final composition, several sources about both the main and many neighboring topics had to be studied. The tools given here can bring interested readers to the further study of gigantic problems such as the restricted three body problem, perturbation theory, and infinite dimensional integrable systems.

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Ignasi Mundet i Riera

Subject

Sistemes hamiltonians, Treballs de fi de grau, Geometria simplèctica, Topologia, Mecànica

Subject (English)

Hamiltonian systems, Bachelor's theses, Symplectic geometry, Topology, Mechanics

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

GIL FUSTER, Elies M. Completely integrable systems on hamiltonian mechanics. [consulted: 17 of June of 2026]. Available at: https://hdl.handle.net/2445/126669

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