Estudi de camps vectorials polinomials mitjançant la compactificació de Poincaré

Abstract

[en] The study of solutions escaping to infinity is an important tool in order to understand the global portrait of a dynamical system in $\mathbb{R}^n$. The Poincaré compactification, which is a method to extend analytically a vector field in a compact manifold (in fact, to an sphere), is one of the most used methods to study the dynamic of vector fields in a neighbourhood of infinity. The main purpose of the project is to follow the path of its construction not only in the euclidean plane (in where it is most used), but also in the $n$-dimensional euclidean space, to end up applying it in the study of several dynamical systems.