Formas normais de sistemas forçados

• Autor(a) principal: Herrera, Yovani Adolfo Villanueva
• Data de Publicação: 2017
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/0013000009bcp
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/7476
• topic: Singularidade; Germe de funções diferenciáveis; Formas diferenciais; Espaço de jatos; Sistemas forçados; Formas normais; Equivalência topológica; Estabilidade estrutural; Singularity; Germ of differential maps; Differential forms; Space of jets; Constrained systems; Normal forms; Topological equivalence; Structural stability; GEOMETRIA E TOPOLOGIA::SISTEMAS DINAMICOS

The subject of this work is the theory of normal forms of smooth vector fields of constrained systems (systems of non-linear differential-algebraic equations). In this study we introduce the qualitative theory of ordinary differential equations, with topics such as stability, structural stability, bifurcations, limit cycles and catastrophes of differential equations, and the functional singularity theory. The goal of this work is classify and normalize constrained systems, first of all from the local point of view, we'll show an idea of the global one and our final objective will be extend this theory to differenciable manifolds of dimension $n \geq 2$.