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
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.
id UFG-2_8fbea228b9b9c9baef669fe30a5c4419
oai_identifier_str oai:repositorio.bc.ufg.br:tede/10493
network_acronym_str UFG-2
network_name_str Repositório Institucional da UFG
repository_id_str
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:/38995/0013000000mwqThe 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). 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) Previous issue date: 2020-02-28Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPqapplication/pdfengUniversidade Federal de GoiásPrograma de Pós-graduação em Matemática (IME)UFGBrasilInstituto de Matemática e Estatística - IME (RG)http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessTeoria dos sistemas dinâmicosTeoria de MorseÍndice de ConleyMatriz de conexãoMatriz de transição direcionalTheory of dynamical systemsMorse theoryConley indexConnection matrixDirectional transition matrixCIENCIAS EXATAS E DA TERRA::MATEMATICADirectional transition matrixMatriz de transição direcionalinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis6600717948137941247600600600600-4268777512335152015-7090823417984401694-2555911436985713659reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; charset=utf-82165http://repositorio.bc.ufg.br/tede/bitstreams/cba7cf49-6d66-4c78-9618-bb5997158120/downloadbd3efa91386c1718a7f26a329fdcb468MD51CC-LICENSElicense_urllicense_urltext/plain; charset=utf-849http://repositorio.bc.ufg.br/tede/bitstreams/51cc760f-552b-4dd6-8976-188fe917d8cf/download4afdbb8c545fd630ea7db775da747b2fMD52license_textlicense_texttext/html; charset=utf-80http://repositorio.bc.ufg.br/tede/bitstreams/a19a4900-c353-44a2-9c8f-490093a44873/downloadd41d8cd98f00b204e9800998ecf8427eMD53license_rdflicense_rdfapplication/rdf+xml; charset=utf-80http://repositorio.bc.ufg.br/tede/bitstreams/35d66238-7a1b-4bcd-9382-2eaa7524ece9/downloadd41d8cd98f00b204e9800998ecf8427eMD54ORIGINALDissertação - Cícero Rumão Gonçalves de Sousa Junior - 2020.pdfDissertação - Cícero Rumão Gonçalves de Sousa Junior - 2020.pdfapplication/pdf1193236http://repositorio.bc.ufg.br/tede/bitstreams/0ca5977a-2975-4c47-9c03-5796ccc9514c/download0a3fe5850508da8da10646a5cf6878d5MD55tede/104932020-04-03 07:46:17.199http://creativecommons.org/licenses/by-nc-nd/4.0/Acesso Abertoopen.accessoai:repositorio.bc.ufg.br:tede/10493http://repositorio.bc.ufg.br/tedeRepositório InstitucionalPUBhttp://repositorio.bc.ufg.br/oai/requesttasesdissertacoes.bc@ufg.bropendoar:2020-04-03T10:46:17Repositório Institucional da UFG - Universidade Federal de Goiás (UFG)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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
format masterThesis
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:/38995/0013000000mwq
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:/38995/0013000000mwq
url http://repositorio.bc.ufg.br/tede/handle/tede/10493
dc.language.iso.fl_str_mv eng
language eng
dc.relation.program.fl_str_mv 6600717948137941247
dc.relation.confidence.fl_str_mv 600
600
600
600
dc.relation.department.fl_str_mv -4268777512335152015
dc.relation.cnpq.fl_str_mv -7090823417984401694
dc.relation.sponsorship.fl_str_mv -2555911436985713659
dc.rights.driver.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
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
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFG
instname:Universidade Federal de Goiás (UFG)
instacron:UFG
instname_str Universidade Federal de Goiás (UFG)
instacron_str UFG
institution UFG
reponame_str Repositório Institucional da UFG
collection Repositório Institucional da UFG
bitstream.url.fl_str_mv http://repositorio.bc.ufg.br/tede/bitstreams/cba7cf49-6d66-4c78-9618-bb5997158120/download
http://repositorio.bc.ufg.br/tede/bitstreams/51cc760f-552b-4dd6-8976-188fe917d8cf/download
http://repositorio.bc.ufg.br/tede/bitstreams/a19a4900-c353-44a2-9c8f-490093a44873/download
http://repositorio.bc.ufg.br/tede/bitstreams/35d66238-7a1b-4bcd-9382-2eaa7524ece9/download
http://repositorio.bc.ufg.br/tede/bitstreams/0ca5977a-2975-4c47-9c03-5796ccc9514c/download
bitstream.checksum.fl_str_mv bd3efa91386c1718a7f26a329fdcb468
4afdbb8c545fd630ea7db775da747b2f
d41d8cd98f00b204e9800998ecf8427e
d41d8cd98f00b204e9800998ecf8427e
0a3fe5850508da8da10646a5cf6878d5
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositório Institucional da UFG - Universidade Federal de Goiás (UFG)
repository.mail.fl_str_mv tasesdissertacoes.bc@ufg.br
_version_ 1811721320391507968

Registros relacionados