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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| Format: | master thesis |
| Status: | Published version |
| Publication Date: | 2018 |
| Country: | Brasil |
| Institution: | Universidade Federal de Goiás (UFG) |
| Repository: | Repositório Institucional da UFG |
| Language: | Portuguese |
| OAI Identifier: | oai:repositorio.bc.ufg.br:tede/8900 |
| Online Access: | http://repositorio.bc.ufg.br/tede/handle/tede/8900 |
| Access Level: | Open access |
| Keyword: | 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 |
| Summary: | 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. |
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