Abundância de operadores lineares transitivos em dimensão infinita.

Detalhes bibliográficos
Autor(a) principal: Kawahama, Felipe Hikari [UNIFESP]
Data de Publicação: 2022
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UNIFESP
Texto Completo: https://repositorio.unifesp.br/11600/67271
Resumo: A teoria de Sistemas Dinâmicos estuda o comportamento de fenômenos em um conjunto no decorrer do tempo e se interessa majoritariamente em sistemas com um certo grau de desordem e imprevisibilidade. Essas propriedades geralmente não são associadas a ação de operadores lineares em espaços vetoriais e com razão em dimensão finita: não existem operadores transitivos nesses espaços. Contudo, em espaços de dimensão infinita existem operadores com as mesmas propriedades encontradas em dinâmicas contínuas e ergódicas em espaços métricos compactos não lineares. Além dessas propriedades, também é de interesse da área de Sistemas Dinâmicos se propriedades dinâmicas interessantes de funções são mantidas para perturbações suficientemente próximas. Embora seja sabido que no caso linear isso nem sempre seja verdade, é possível definir uma classe aberta de operadores com ricas propriedades dinâmicas quando restringimos seu domínio.
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spelling Kawahama, Felipe Hikari [UNIFESP]http://lattes.cnpq.br/8567826495956662http://lattes.cnpq.br/8477080812857959Cirilo, Patricia Romano [UNIFESP]São José dos Campos, SP2023-03-21T17:01:40Z2023-03-21T17:01:40Z2022-11-04https://repositorio.unifesp.br/11600/67271A teoria de Sistemas Dinâmicos estuda o comportamento de fenômenos em um conjunto no decorrer do tempo e se interessa majoritariamente em sistemas com um certo grau de desordem e imprevisibilidade. Essas propriedades geralmente não são associadas a ação de operadores lineares em espaços vetoriais e com razão em dimensão finita: não existem operadores transitivos nesses espaços. Contudo, em espaços de dimensão infinita existem operadores com as mesmas propriedades encontradas em dinâmicas contínuas e ergódicas em espaços métricos compactos não lineares. Além dessas propriedades, também é de interesse da área de Sistemas Dinâmicos se propriedades dinâmicas interessantes de funções são mantidas para perturbações suficientemente próximas. Embora seja sabido que no caso linear isso nem sempre seja verdade, é possível definir uma classe aberta de operadores com ricas propriedades dinâmicas quando restringimos seu domínio.The Dynamical Systems theory studies the behaviour of phenomena acting on sets through time and in most cases it takes interest in systems with a certain degree of unorderedness and unpredictability. These properties are not generally associated to the actions of linear operators in vector spaces and in finite dimensional ones there is a reason for that: there are no transitive operators in these spaces. However, in infinite dimensional vector spaces there are operators with the same dynamical properties as the ones found in continuous and ergodic dynamics in non-linear compact metric spaces. Besides these properties, the Dynamical Systems theory also takes interest in whether interesting dynamical properties of a certain function are preserved under sufficiently small perturbations. Even though it is known that, in the linear context, this is not generally the case, it is possible to define an open class of operators where each one of them has rich dynamical properties when its domain is restricted.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)2019/20500-4126 fporUniversidade Federal de São PauloDinâmica LinearCaosRobustezAbundância de operadores lineares transitivos em dimensão infinita.Abundance of transitive linear operators in infinite dimension.info: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 AplicadaGeometria e DinâmicaORIGINALDisserta__o__Mestrado_.pdfDisserta__o__Mestrado_.pdfapplication/pdf1599456${dspace.ui.url}/bitstream/11600/67271/1/Disserta__o__Mestrado_.pdf27050619d97618f5d49157855684c985MD51open 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InstitucionalPUBhttp://www.repositorio.unifesp.br/oai/requestopendoar:34652023-10-26T04:00:48Repositório Institucional da UNIFESP - Universidade Federal de São Paulo (UNIFESP)false
dc.title.pt_BR.fl_str_mv Abundância de operadores lineares transitivos em dimensão infinita.
dc.title.alternative.pt_BR.fl_str_mv Abundance of transitive linear operators in infinite dimension.
title Abundância de operadores lineares transitivos em dimensão infinita.
spellingShingle Abundância de operadores lineares transitivos em dimensão infinita.
Kawahama, Felipe Hikari [UNIFESP]
Dinâmica Linear
Caos
Robustez
title_short Abundância de operadores lineares transitivos em dimensão infinita.
title_full Abundância de operadores lineares transitivos em dimensão infinita.
title_fullStr Abundância de operadores lineares transitivos em dimensão infinita.
title_full_unstemmed Abundância de operadores lineares transitivos em dimensão infinita.
title_sort Abundância de operadores lineares transitivos em dimensão infinita.
author Kawahama, Felipe Hikari [UNIFESP]
author_facet Kawahama, Felipe Hikari [UNIFESP]
author_role author
dc.contributor.authorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/8567826495956662
dc.contributor.advisorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/8477080812857959
dc.contributor.author.fl_str_mv Kawahama, Felipe Hikari [UNIFESP]
dc.contributor.advisor1.fl_str_mv Cirilo, Patricia Romano [UNIFESP]
contributor_str_mv Cirilo, Patricia Romano [UNIFESP]
dc.subject.por.fl_str_mv Dinâmica Linear
Caos
Robustez
topic Dinâmica Linear
Caos
Robustez
description A teoria de Sistemas Dinâmicos estuda o comportamento de fenômenos em um conjunto no decorrer do tempo e se interessa majoritariamente em sistemas com um certo grau de desordem e imprevisibilidade. Essas propriedades geralmente não são associadas a ação de operadores lineares em espaços vetoriais e com razão em dimensão finita: não existem operadores transitivos nesses espaços. Contudo, em espaços de dimensão infinita existem operadores com as mesmas propriedades encontradas em dinâmicas contínuas e ergódicas em espaços métricos compactos não lineares. Além dessas propriedades, também é de interesse da área de Sistemas Dinâmicos se propriedades dinâmicas interessantes de funções são mantidas para perturbações suficientemente próximas. Embora seja sabido que no caso linear isso nem sempre seja verdade, é possível definir uma classe aberta de operadores com ricas propriedades dinâmicas quando restringimos seu domínio.
publishDate 2022
dc.date.issued.fl_str_mv 2022-11-04
dc.date.accessioned.fl_str_mv 2023-03-21T17:01:40Z
dc.date.available.fl_str_mv 2023-03-21T17:01:40Z
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
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