Simmetries in binary differential equations
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da USP |
Texto Completo: | https://doi.org/10.11606/T.55.2017.tde-11072017-170308 |
Resumo: | The purpose of this thesis in to introduce the systematic study of symmetries in binary differential equations (BDEs). We formalize the concept of a symmetric BDE, under the linear action of a compact Lie group. One of the main results establishes a formula that relates the algebraic and geometric effects of the occurrence of the symmetry in the problem. Using tools from invariant theory and representation theory for compact Lie groups we deduce the general forms of equivariant binary differential equations under compact subgroups of O(2). A study about the behavior of the invariant straight lines on the configuration of homogeneous BDEs of degree n is done with emphasis on cases in which n = 0 and n = 1. Also for the linear case (n = 1) the equivariant normal forms are presented. Symmetries of linear 1-forms are also studied and related with symmetries of tangent orthogonal vectors fields associated with it. |
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oai:teses.usp.br:tde-11072017-170308 |
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Biblioteca Digital de Teses e Dissertações da USP |
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info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis Simmetries in binary differential equations Simetrias em equações diferenciais binárias 2017-04-28Miriam Garcia ManoelPatricia Hernandes BaptistelliRonaldo Alves GarciaIsabel Salgado LabouriauFarid TariPatricia TempestaUniversidade de São PauloMatemáticaUSPBR 1-forma quadratica equivariante Binary differential equation Compact Lie group Equação diferencial binária Equivariant quadratic 1-form Grupo de Lie compacto Representation theory Simetria Symmetry Teoria de representação The purpose of this thesis in to introduce the systematic study of symmetries in binary differential equations (BDEs). We formalize the concept of a symmetric BDE, under the linear action of a compact Lie group. One of the main results establishes a formula that relates the algebraic and geometric effects of the occurrence of the symmetry in the problem. Using tools from invariant theory and representation theory for compact Lie groups we deduce the general forms of equivariant binary differential equations under compact subgroups of O(2). A study about the behavior of the invariant straight lines on the configuration of homogeneous BDEs of degree n is done with emphasis on cases in which n = 0 and n = 1. Also for the linear case (n = 1) the equivariant normal forms are presented. Symmetries of linear 1-forms are also studied and related with symmetries of tangent orthogonal vectors fields associated with it. O objetivo desta tese é introduzir o estudo sistemático de simetrias em equações diferenciais binárias (EDBs). Neste trabalho formalizamos o conceito de EDB simétrica sobre a ação de um grupo de Lie compacto. Um dos principais resultados é uma fórmula que relaciona o efeito geométrico e algébrico das simetrias presentes no problema. Utilizando ferramentas da teoria invariante e de representação para grupos compactos deduzimos as formas gerais para EDBs equivariantes. Um estudo sobre o comportamento das retas invariantes na configuração de EDBs com coeficientes homogêneos de grau n é feito com ênfase nos casos de grau 0 e 1, ainda no caso de grau 1 são apresentadas suas formas normais. Simetrias de 1-formas lineares são também estudadas e relacionadas com as simetrias dos seus campos tangente e ortogonal. https://doi.org/10.11606/T.55.2017.tde-11072017-170308info:eu-repo/semantics/openAccessengreponame:Biblioteca Digital de Teses e Dissertações da USPinstname:Universidade de São Paulo (USP)instacron:USP2023-12-21T18:42:31Zoai:teses.usp.br:tde-11072017-170308Biblioteca Digital de Teses e Dissertaçõeshttp://www.teses.usp.br/PUBhttp://www.teses.usp.br/cgi-bin/mtd2br.plvirginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.bropendoar:27212023-12-22T12:30:04.349362Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP)false |
dc.title.en.fl_str_mv |
Simmetries in binary differential equations |
dc.title.alternative.pt.fl_str_mv |
Simetrias em equações diferenciais binárias |
title |
Simmetries in binary differential equations |
spellingShingle |
Simmetries in binary differential equations Patricia Tempesta |
title_short |
Simmetries in binary differential equations |
title_full |
Simmetries in binary differential equations |
title_fullStr |
Simmetries in binary differential equations |
title_full_unstemmed |
Simmetries in binary differential equations |
title_sort |
Simmetries in binary differential equations |
author |
Patricia Tempesta |
author_facet |
Patricia Tempesta |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Miriam Garcia Manoel |
dc.contributor.referee1.fl_str_mv |
Patricia Hernandes Baptistelli |
dc.contributor.referee2.fl_str_mv |
Ronaldo Alves Garcia |
dc.contributor.referee3.fl_str_mv |
Isabel Salgado Labouriau |
dc.contributor.referee4.fl_str_mv |
Farid Tari |
dc.contributor.author.fl_str_mv |
Patricia Tempesta |
contributor_str_mv |
Miriam Garcia Manoel Patricia Hernandes Baptistelli Ronaldo Alves Garcia Isabel Salgado Labouriau Farid Tari |
description |
The purpose of this thesis in to introduce the systematic study of symmetries in binary differential equations (BDEs). We formalize the concept of a symmetric BDE, under the linear action of a compact Lie group. One of the main results establishes a formula that relates the algebraic and geometric effects of the occurrence of the symmetry in the problem. Using tools from invariant theory and representation theory for compact Lie groups we deduce the general forms of equivariant binary differential equations under compact subgroups of O(2). A study about the behavior of the invariant straight lines on the configuration of homogeneous BDEs of degree n is done with emphasis on cases in which n = 0 and n = 1. Also for the linear case (n = 1) the equivariant normal forms are presented. Symmetries of linear 1-forms are also studied and related with symmetries of tangent orthogonal vectors fields associated with it. |
publishDate |
2017 |
dc.date.issued.fl_str_mv |
2017-04-28 |
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://doi.org/10.11606/T.55.2017.tde-11072017-170308 |
url |
https://doi.org/10.11606/T.55.2017.tde-11072017-170308 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade de São Paulo |
dc.publisher.program.fl_str_mv |
Matemática |
dc.publisher.initials.fl_str_mv |
USP |
dc.publisher.country.fl_str_mv |
BR |
publisher.none.fl_str_mv |
Universidade de São Paulo |
dc.source.none.fl_str_mv |
reponame:Biblioteca Digital de Teses e Dissertações da USP instname:Universidade de São Paulo (USP) instacron:USP |
instname_str |
Universidade de São Paulo (USP) |
instacron_str |
USP |
institution |
USP |
reponame_str |
Biblioteca Digital de Teses e Dissertações da USP |
collection |
Biblioteca Digital de Teses e Dissertações da USP |
repository.name.fl_str_mv |
Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP) |
repository.mail.fl_str_mv |
virginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.br |
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1794502656689963008 |