Fontich, Ernest, 1955-Garriga i Xirgu, Meritxell2022-04-252022-04-252021-06-20https://hdl.handle.net/2445/185116Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Ernest Fontich[en] In this project we will study the parameterization method for invariant manifolds of discrete dynamical systems, a method introduced by X. Cabré, E. Fontich and R. de la Llave in [1, 2]. From a theoretical point of view, we will study and demonstrate the parameterization method for 1-dimensional invariant manifolds, presenting first of all the necessary results to develop this method. Then, from a more practical point of view, we will use the programming language C to create a program that uses the parameterization method to find different 1-dimensional invariant manifolds, applying it on two discrete dynamical systems.62 p.application/pdfcatcc-by-nc-nd (c) Meritxell Garriga i Xirgu, 2021http://creativecommons.org/licenses/by-nc-nd/3.0/es/Espais de BanachTreballs de fi de grauAnàlisi funcionalSistemes dinàmics diferenciablesTeoria d'operadorsBanach spacesBachelor's thesesFunctional analysisDifferentiable dynamical systemsOperator theoryinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess