Índice de Conley para atratores de inclusão diferencial

• Autor(a) principal: Queiroz, Lenison Alves de
• Data de Publicação: 2018
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/8900
• topic: Equações diferenciais; Pontos de equilíbrio; Índice homológico; Índice de Conley; Índice de Morse; Differential equations; Equilibrium points; Homology index; Conley index; Morse index; GEOMETRIA E TOPOLOGIA::SISTEMAS DINAMICOS

The present work deals with mathematical themes called Conley’s theory, differential inclu- sions and Morse theory inserted in this variant is the topological invariant for the region of discontinuity, the Conley index of discontinuous vector fields, where the discontinuities are concentrated on a surface. With this invariant it is possible to predict bifurcation results, as well as results of regularization of the discontinuous field. In Conley’s Theory, one doesn’t investigate only a single invariant set in a system; on the contrary, it is a decomposition of an invariant set into several “smaller” invariant subsets along with the orbits that connect these subsets. The methodology adopted for the research was based on the deductive analy- sis, a method that allowed the determination of the Conley index using tools of differential inclusions, index-pair and Morse theory to arrive at the determination of the homological in- dex.