Linearização de campos de vetores

Abstract

This work aims to study some fundamental results in Dynamical Systems, mainly about the linearization of vector fields, that is, to find conjugations between the field and its linear part in the neighborhood of certain points. To start, we present the Stable Manifold Theorem for fields. Finally, we present the Poincaré Linearization Theorem for fields and a version of the Guillemin-Sternberg commutativity criterion for families of vector fields with a common null critical point. We also have a appendix, briefly presenting the Hartman-Grobman Theorems, which show definitively that vector fields and diffeomorphisms are conjugated to their derivatives in the vicinity of a hyperbolic singularity