Generic dynamics for evolution groups and $C_0$-semigroups on Hilbert spaces
| Ano de defesa: | 2019 |
|---|---|
| Autor(a) principal: | |
| Orientador(a): | |
| Banca de defesa: | |
| Tipo de documento: | Tese |
| Tipo de acesso: | Acesso aberto |
| Idioma: | eng |
| Instituição de defesa: |
Universidade Federal de Minas Gerais
|
| Programa de Pós-Graduação: |
Não Informado pela instituição
|
| Departamento: |
Não Informado pela instituição
|
| País: |
Não Informado pela instituição
|
| Palavras-chave em Português: | |
| Link de acesso: | https://hdl.handle.net/1843/EABA-BCTFV3 |
Resumo: | In this thesis, we study the typical behaviour (from the topological viewpoint) of the decaying rates of the orbits of unitary evolution groups and C0-semigroups on Hilbert spaces. We have found that: (1) some dynamical quantities related to evolution groups have an oscillating behaviour between a polynomially rapid decay and an arbitrarily slowdecay; (2) the decaying rates of each typical orbit, in Baires sense, of C0-semigroups which are stable but not exponentially stable depend on sequences of time going to infinity. The proofs are based on the relations between such decaying rates and some spectral properties of their respective generators |
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2019-08-10T00:26:41Z2025-09-08T22:56:02Z2019-08-10T00:26:41Z2019-05-10https://hdl.handle.net/1843/EABA-BCTFV3In this thesis, we study the typical behaviour (from the topological viewpoint) of the decaying rates of the orbits of unitary evolution groups and C0-semigroups on Hilbert spaces. We have found that: (1) some dynamical quantities related to evolution groups have an oscillating behaviour between a polynomially rapid decay and an arbitrarily slowdecay; (2) the decaying rates of each typical orbit, in Baires sense, of C0-semigroups which are stable but not exponentially stable depend on sequences of time going to infinity. The proofs are based on the relations between such decaying rates and some spectral properties of their respective generatorsUniversidade Federal de Minas GeraisdecaimentoMatemáticaGeneric dynamics for evolution groups and $C_0$-semigroups on Hilbert spacesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisMoacir Aloisio Nascimento dos Santosinfo:eu-repo/semantics/openAccessengreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGSilas Luiz de CarvalhoLuiz Gustavo Farah DiasMarcos da Silva MontenegroCésar Rogério de OliveiraPedro LopesNesta tese, estudamos o comportamento típico (do ponto de vista topológico) das taxas de decaimento das órbitas de grupos unitários de evolução e C0-semigrupos em espaços de Hilbert. Encontramos que: (1) algumas quantidades dinâmicas relacionadas aos grupos de evolução tem um comportamento oscilando entre um decaimento polinomialmente rápido e um decaimento arbitrariamente lento; (2) as taxas de decaimento de cada órbita típica, no sentido de Baire, de C0-semigrupos que são estáveis mas não exponencialmente estáveis dependem de sequências do tempo que vão para infinito. As provas são baseadas nas relações existentes entre essas taxas de decaimento e propriedades espectrais dos respectivos geradores.UFMGORIGINALtese_moacir.pdfapplication/pdf558137https://repositorio.ufmg.br//bitstreams/de6e517c-adf8-47c8-9af8-d299dfe5fb9c/download1113e1f912a5e94b4f6ff5fb60f8ef1bMD51trueAnonymousREADTEXTtese_moacir.pdf.txttext/plain125196https://repositorio.ufmg.br//bitstreams/421b8459-7229-47a8-83e0-ddc3b29c6797/download4681882319e84deb9c8ea0d8645a9ea7MD52falseAnonymousREAD1843/EABA-BCTFV32025-09-08 19:56:02.694open.accessoai:repositorio.ufmg.br:1843/EABA-BCTFV3https://repositorio.ufmg.br/Repositório InstitucionalPUBhttps://repositorio.ufmg.br/oairepositorio@ufmg.bropendoar:2025-09-08T22:56:02Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false |
| dc.title.none.fl_str_mv |
Generic dynamics for evolution groups and $C_0$-semigroups on Hilbert spaces |
| title |
Generic dynamics for evolution groups and $C_0$-semigroups on Hilbert spaces |
| spellingShingle |
Generic dynamics for evolution groups and $C_0$-semigroups on Hilbert spaces Moacir Aloisio Nascimento dos Santos Matemática decaimento |
| title_short |
Generic dynamics for evolution groups and $C_0$-semigroups on Hilbert spaces |
| title_full |
Generic dynamics for evolution groups and $C_0$-semigroups on Hilbert spaces |
| title_fullStr |
Generic dynamics for evolution groups and $C_0$-semigroups on Hilbert spaces |
| title_full_unstemmed |
Generic dynamics for evolution groups and $C_0$-semigroups on Hilbert spaces |
| title_sort |
Generic dynamics for evolution groups and $C_0$-semigroups on Hilbert spaces |
| author |
Moacir Aloisio Nascimento dos Santos |
| author_facet |
Moacir Aloisio Nascimento dos Santos |
| author_role |
author |
| dc.contributor.author.fl_str_mv |
Moacir Aloisio Nascimento dos Santos |
| dc.subject.por.fl_str_mv |
Matemática |
| topic |
Matemática decaimento |
| dc.subject.other.none.fl_str_mv |
decaimento |
| description |
In this thesis, we study the typical behaviour (from the topological viewpoint) of the decaying rates of the orbits of unitary evolution groups and C0-semigroups on Hilbert spaces. We have found that: (1) some dynamical quantities related to evolution groups have an oscillating behaviour between a polynomially rapid decay and an arbitrarily slowdecay; (2) the decaying rates of each typical orbit, in Baires sense, of C0-semigroups which are stable but not exponentially stable depend on sequences of time going to infinity. The proofs are based on the relations between such decaying rates and some spectral properties of their respective generators |
| publishDate |
2019 |
| dc.date.accessioned.fl_str_mv |
2019-08-10T00:26:41Z 2025-09-08T22:56:02Z |
| dc.date.available.fl_str_mv |
2019-08-10T00:26:41Z |
| dc.date.issued.fl_str_mv |
2019-05-10 |
| dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
| dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
| format |
doctoralThesis |
| status_str |
publishedVersion |
| dc.identifier.uri.fl_str_mv |
https://hdl.handle.net/1843/EABA-BCTFV3 |
| url |
https://hdl.handle.net/1843/EABA-BCTFV3 |
| dc.language.iso.fl_str_mv |
eng |
| language |
eng |
| dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
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openAccess |
| dc.publisher.none.fl_str_mv |
Universidade Federal de Minas Gerais |
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Universidade Federal de Minas Gerais |
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reponame:Repositório Institucional da UFMG instname:Universidade Federal de Minas Gerais (UFMG) instacron:UFMG |
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