Operadores hipercíclicos em espaços de Banach
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2020 |
| Tipo de documento: | Dissertação |
| Idioma: | por |
| Título da fonte: | Repositório Institucional da UNIFESP |
| Texto Completo: | https://repositorio.unifesp.br/xmlui/handle/11600/62234 https://sucupira.capes.gov.br/sucupira/public/consultas/coleta/trabalhoConclusao/viewTrabalhoConclusao.jsf?popup=true&id_trabalho=10404186 |
Resumo: | Nesta dissertação tratamos da dinâmica de operadores lineares em espaços de Banach, sob o aspecto de hiperciclicidade. Estudamos em quais condições o fenômeno da hiperciclicidade se apresenta e relacionamos com outros fenômenos que ocorrem na dinâmica de operadores como transitividade topológica, topologicamente mixing, topologicamente weakly mixing e caoticidade (caos no sentido de Devaney). Estudamos a relação do Teorema da Transitividade de Birkhoff e a hiperciclicidade. Mostraremos o Critério de Hiperciclicidade como condição suficiente para determinar se um operador definido em um espaço de Banach é hipercíclico. Além disso apresentaremos alguns exemplos clássicos de operadores que são hipercíclicos e, ao final, o Teorema de Bès-Peris. |
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Salcedo, Anderson Jose Mercado [UNIFESP]http://lattes.cnpq.br/5964284694957893http://lattes.cnpq.br/8477080812857959Cirilo, Patricia Romano [UNIFESP]Sao José dos Campos, SP2021-11-16T17:59:30Z2021-11-16T17:59:30Z2020-12-07Mercado, Anderson. (2020) Operadores hipercíclicos em espaços de Banach. Universidade Federal de São Paulo.https://repositorio.unifesp.br/xmlui/handle/11600/62234https://sucupira.capes.gov.br/sucupira/public/consultas/coleta/trabalhoConclusao/viewTrabalhoConclusao.jsf?popup=true&id_trabalho=10404186Nesta dissertação tratamos da dinâmica de operadores lineares em espaços de Banach, sob o aspecto de hiperciclicidade. Estudamos em quais condições o fenômeno da hiperciclicidade se apresenta e relacionamos com outros fenômenos que ocorrem na dinâmica de operadores como transitividade topológica, topologicamente mixing, topologicamente weakly mixing e caoticidade (caos no sentido de Devaney). Estudamos a relação do Teorema da Transitividade de Birkhoff e a hiperciclicidade. Mostraremos o Critério de Hiperciclicidade como condição suficiente para determinar se um operador definido em um espaço de Banach é hipercíclico. Além disso apresentaremos alguns exemplos clássicos de operadores que são hipercíclicos e, ao final, o Teorema de Bès-Peris.In this dissertation we deal with the dynamics of linear operators in Banach spaces, under the aspect of hypercyclicity. We study under what conditions the phenomenon of hypercyclicity presents itself and relate it to other phenomena that occur in the dynamics of operators such as topological transitivity, topologically mixing, topologically weakly mixing and chaoticity (chaos in the sense of Devaney). We studied the relationship between Birkhoff’s Transitivity Theorem and hypercyclicality. We will show the Hypercyclicity Criterion as a sufficient condition to determine whether an operator defined in a Banach space is hypercyclic. In addition, we will present some classic examples of operators that are hypercyclic and, at the end, the Bès-Peris Theorem.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)60 f.porUniversidade Federal de São PauloOperadores LinearesHiperciclicidadeÓrbitas densasTransitividadeCriterio de HiperciclicidadeOperadores hipercíclicos em espaços de BanachHypercyclic operators in Banach spacesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UNIFESPinstname:Universidade Federal de São Paulo (UNIFESP)instacron:UNIFESPInstituto de Ciência e Tecnologia (ICT)Matemática Pura e AplicadaMatemáticasistemas dinâmicosORIGINALDissertacao_AndersonMercado_assinada.pdfDissertacao_AndersonMercado_assinada.pdfDissertacao Mestradoapplication/pdf2285918${dspace.ui.url}/bitstream/11600/62234/1/Dissertacao_AndersonMercado_assinada.pdf9e11ecf2b398504b7f661a2d831e7c3aMD51open 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InstitucionalPUBhttp://www.repositorio.unifesp.br/oai/requestopendoar:34652023-05-23T05:59:23Repositório Institucional da UNIFESP - Universidade Federal de São Paulo (UNIFESP)false |
| dc.title.pt_BR.fl_str_mv |
Operadores hipercíclicos em espaços de Banach |
| dc.title.alternative.pt_BR.fl_str_mv |
Hypercyclic operators in Banach spaces |
| title |
Operadores hipercíclicos em espaços de Banach |
| spellingShingle |
Operadores hipercíclicos em espaços de Banach Salcedo, Anderson Jose Mercado [UNIFESP] Operadores Lineares Hiperciclicidade Órbitas densas Transitividade Criterio de Hiperciclicidade |
| title_short |
Operadores hipercíclicos em espaços de Banach |
| title_full |
Operadores hipercíclicos em espaços de Banach |
| title_fullStr |
Operadores hipercíclicos em espaços de Banach |
| title_full_unstemmed |
Operadores hipercíclicos em espaços de Banach |
| title_sort |
Operadores hipercíclicos em espaços de Banach |
| author |
Salcedo, Anderson Jose Mercado [UNIFESP] |
| author_facet |
Salcedo, Anderson Jose Mercado [UNIFESP] |
| author_role |
author |
| dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/5964284694957893 |
| dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/8477080812857959 |
| dc.contributor.author.fl_str_mv |
Salcedo, Anderson Jose Mercado [UNIFESP] |
| dc.contributor.advisor1.fl_str_mv |
Cirilo, Patricia Romano [UNIFESP] |
| contributor_str_mv |
Cirilo, Patricia Romano [UNIFESP] |
| dc.subject.por.fl_str_mv |
Operadores Lineares Hiperciclicidade Órbitas densas Transitividade Criterio de Hiperciclicidade |
| topic |
Operadores Lineares Hiperciclicidade Órbitas densas Transitividade Criterio de Hiperciclicidade |
| description |
Nesta dissertação tratamos da dinâmica de operadores lineares em espaços de Banach, sob o aspecto de hiperciclicidade. Estudamos em quais condições o fenômeno da hiperciclicidade se apresenta e relacionamos com outros fenômenos que ocorrem na dinâmica de operadores como transitividade topológica, topologicamente mixing, topologicamente weakly mixing e caoticidade (caos no sentido de Devaney). Estudamos a relação do Teorema da Transitividade de Birkhoff e a hiperciclicidade. Mostraremos o Critério de Hiperciclicidade como condição suficiente para determinar se um operador definido em um espaço de Banach é hipercíclico. Além disso apresentaremos alguns exemplos clássicos de operadores que são hipercíclicos e, ao final, o Teorema de Bès-Peris. |
| publishDate |
2020 |
| dc.date.issued.fl_str_mv |
2020-12-07 |
| dc.date.accessioned.fl_str_mv |
2021-11-16T17:59:30Z |
| dc.date.available.fl_str_mv |
2021-11-16T17:59:30Z |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/masterThesis |
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masterThesis |
| status_str |
publishedVersion |
| dc.identifier.citation.fl_str_mv |
Mercado, Anderson. (2020) Operadores hipercíclicos em espaços de Banach. Universidade Federal de São Paulo. |
| dc.identifier.uri.fl_str_mv |
https://repositorio.unifesp.br/xmlui/handle/11600/62234 https://sucupira.capes.gov.br/sucupira/public/consultas/coleta/trabalhoConclusao/viewTrabalhoConclusao.jsf?popup=true&id_trabalho=10404186 |
| identifier_str_mv |
Mercado, Anderson. (2020) Operadores hipercíclicos em espaços de Banach. Universidade Federal de São Paulo. |
| url |
https://repositorio.unifesp.br/xmlui/handle/11600/62234 https://sucupira.capes.gov.br/sucupira/public/consultas/coleta/trabalhoConclusao/viewTrabalhoConclusao.jsf?popup=true&id_trabalho=10404186 |
| dc.language.iso.fl_str_mv |
por |
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por |
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info:eu-repo/semantics/openAccess |
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openAccess |
| dc.format.none.fl_str_mv |
60 f. |
| dc.coverage.spatial.pt_BR.fl_str_mv |
Sao José dos Campos, SP |
| dc.publisher.none.fl_str_mv |
Universidade Federal de São Paulo |
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Universidade Federal de São Paulo |
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reponame:Repositório Institucional da UNIFESP instname:Universidade Federal de São Paulo (UNIFESP) instacron:UNIFESP |
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Universidade Federal de São Paulo (UNIFESP) |
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