Índice de Conley para atratores de inclusão diferencial

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 s...

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Detalles Bibliográficos
Autor: Queiroz, Lenison Alves de
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2018
País:Brasil
Institución:Universidade Federal de Goiás (UFG)
Repositorio:Repositório Institucional da UFG
Idioma:portugués
OAI Identifier:oai:repositorio.bc.ufg.br:tede/8900
Acceso en línea:http://repositorio.bc.ufg.br/tede/handle/tede/8900
Access Level:acceso abierto
Palabra clave: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
Descripción
Sumario: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.