Índice de Conley para atratores de inclusão diferencial
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2018-08-20
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Universidade Federal de Goiás
Resumo
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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QUERIOZ, Lenison Alves de. Índice de Conley para atratores de inclusão diferencial. 2018. 60 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2018.