Directional transition matrix

Detalhes bibliográficos
Autor(a) principal: Sousa Junior, Cícero Rumão Gonçalves de
Data de Publicação: 2020
Tipo de documento: Dissertação
Idioma: eng
Título da fonte: Repositório Institucional da UFG
dARK ID: ark:/38995/0013000000909
Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/10493
Resumo: The study of global bifurcations in dynamical systems can be quite complicated, so some topological tools are very effective at detecting these bifurcations, between them a very prominent tool is the Conley index theory applied to transition matrices. Thus, we explore the main properties and the main mathematical objects necessary for the study of these matrices, with the objective find a new way of obtaining the directional transition matrix without dependence on slow dynamics. Finally, we present a new algorithm that reduces the amount of computation needed to obtain the directional transition matrix.
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spelling Vieira, Ewerton Rochahttp://lattes.cnpq.br/9011778118531233Vieira, Ewerton RochaLima, Dahisy Valadão de SouzaEuzébio, Rodrigo Donizetehttp://lattes.cnpq.br/8262143167778154Sousa Junior, Cícero Rumão Gonçalves de2020-04-03T10:46:17Z2020-02-28SOUSA JUNIOR, C. R. G. Directional transition matrix. 2020.58 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2020.http://repositorio.bc.ufg.br/tede/handle/tede/10493ark:/38995/0013000000909The study of global bifurcations in dynamical systems can be quite complicated, so some topological tools are very effective at detecting these bifurcations, between them a very prominent tool is the Conley index theory applied to transition matrices. Thus, we explore the main properties and the main mathematical objects necessary for the study of these matrices, with the objective find a new way of obtaining the directional transition matrix without dependence on slow dynamics. Finally, we present a new algorithm that reduces the amount of computation needed to obtain the directional transition matrix.O estudo de bifurcações globais em sistemas dinâmicos pode ser bastante complicado, então algumas ferramentas topológicas são bastante eficazes na detecção dessas bifurcações, entre elas uma ferramenta muito proeminente é a teoria do índice de Conley aplicado as matrizes de transição. Exploramos assim as principais propriedades e os principais objetos matemáticos necessários para o estudo dessas matrizes, com o objetivo de encontrar uma nova maneira de obter a matriz de transição direcional sem a dependência de uma dinâmica lenta. Por fim apresentamos um novo algoritmo que reduz a quantidade de cálculos necessários para obter a matriz de transição direcional.Submitted by Franciele Moreira (francielemoreyra@gmail.com) on 2020-04-01T15:17:53Z No. of bitstreams: 2 Dissertação - Cícero Rumão Gonçalves de Sousa Junior - 2020.pdf: 1193236 bytes, checksum: 0a3fe5850508da8da10646a5cf6878d5 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Rejected by Luciana Ferreira (lucgeral@gmail.com), reason: Temos que mudar o campo de idioma, o qual já aparece preenchido. on 2020-04-02T10:42:39Z (GMT)Submitted by Franciele Moreira (francielemoreyra@gmail.com) on 2020-04-02T23:06:53Z No. of bitstreams: 2 Dissertação - Cícero Rumão Gonçalves de Sousa Junior - 2020.pdf: 1193236 bytes, checksum: 0a3fe5850508da8da10646a5cf6878d5 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2020-04-03T10:46:17Z (GMT) No. of bitstreams: 2 Dissertação - Cícero Rumão Gonçalves de Sousa Junior - 2020.pdf: 1193236 bytes, checksum: 0a3fe5850508da8da10646a5cf6878d5 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Made available in DSpace on 2020-04-03T10:46:17Z (GMT). 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dc.title.eng.fl_str_mv Directional transition matrix
dc.title.alternative.por.fl_str_mv Matriz de transição direcional
title Directional transition matrix
spellingShingle Directional transition matrix
Sousa Junior, Cícero Rumão Gonçalves de
Teoria dos sistemas dinâmicos
Teoria de Morse
Índice de Conley
Matriz de conexão
Matriz de transição direcional
Theory of dynamical systems
Morse theory
Conley index
Connection matrix
Directional transition matrix
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Directional transition matrix
title_full Directional transition matrix
title_fullStr Directional transition matrix
title_full_unstemmed Directional transition matrix
title_sort Directional transition matrix
author Sousa Junior, Cícero Rumão Gonçalves de
author_facet Sousa Junior, Cícero Rumão Gonçalves de
author_role author
dc.contributor.advisor1.fl_str_mv Vieira, Ewerton Rocha
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/9011778118531233
dc.contributor.referee1.fl_str_mv Vieira, Ewerton Rocha
dc.contributor.referee2.fl_str_mv Lima, Dahisy Valadão de Souza
dc.contributor.referee3.fl_str_mv Euzébio, Rodrigo Donizete
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/8262143167778154
dc.contributor.author.fl_str_mv Sousa Junior, Cícero Rumão Gonçalves de
contributor_str_mv Vieira, Ewerton Rocha
Vieira, Ewerton Rocha
Lima, Dahisy Valadão de Souza
Euzébio, Rodrigo Donizete
dc.subject.por.fl_str_mv Teoria dos sistemas dinâmicos
Teoria de Morse
Índice de Conley
Matriz de conexão
Matriz de transição direcional
topic Teoria dos sistemas dinâmicos
Teoria de Morse
Índice de Conley
Matriz de conexão
Matriz de transição direcional
Theory of dynamical systems
Morse theory
Conley index
Connection matrix
Directional transition matrix
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Theory of dynamical systems
Morse theory
Conley index
Connection matrix
Directional transition matrix
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description The study of global bifurcations in dynamical systems can be quite complicated, so some topological tools are very effective at detecting these bifurcations, between them a very prominent tool is the Conley index theory applied to transition matrices. Thus, we explore the main properties and the main mathematical objects necessary for the study of these matrices, with the objective find a new way of obtaining the directional transition matrix without dependence on slow dynamics. Finally, we present a new algorithm that reduces the amount of computation needed to obtain the directional transition matrix.
publishDate 2020
dc.date.accessioned.fl_str_mv 2020-04-03T10:46:17Z
dc.date.issued.fl_str_mv 2020-02-28
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
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status_str publishedVersion
dc.identifier.citation.fl_str_mv SOUSA JUNIOR, C. R. G. Directional transition matrix. 2020.58 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2020.
dc.identifier.uri.fl_str_mv http://repositorio.bc.ufg.br/tede/handle/tede/10493
dc.identifier.dark.fl_str_mv ark:/38995/0013000000909
identifier_str_mv SOUSA JUNIOR, C. R. G. Directional transition matrix. 2020.58 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2020.
ark:/38995/0013000000909
url http://repositorio.bc.ufg.br/tede/handle/tede/10493
dc.language.iso.fl_str_mv eng
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dc.relation.program.fl_str_mv 6600717948137941247
dc.relation.confidence.fl_str_mv 600
600
600
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dc.publisher.none.fl_str_mv Universidade Federal de Goiás
dc.publisher.program.fl_str_mv Programa de Pós-graduação em Matemática (IME)
dc.publisher.initials.fl_str_mv UFG
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv Instituto de Matemática e Estatística - IME (RG)
publisher.none.fl_str_mv Universidade Federal de Goiás
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