Jorba i Monte, ÀngelCamı́ Buzón, Javier2022-09-082022-09-082022-06-13https://hdl.handle.net/2445/188821Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Àngel Jorba i Monte[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.50 p.application/pdfcatcc-by-nc-nd (c) Javier Camı́ Buzón, 2022http://creativecommons.org/licenses/by-nc-nd/3.0/es/Fluxos (Sistemes dinàmics diferenciables)Treballs de fi de grauEspais de BanachSistemes hamiltoniansFlows (Differentiable dynamical systems)Bachelor's thesesBanach spacesHamiltonian systemsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess