El mètode de la parametrització per a varietats invariants d’aplicacions

Abstract

[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.