On the crossing limit cycles for piecewise linear differential systems on the plane
Autor(a) principal: | |
---|---|
Data de Publicação: | 2019 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFG |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/10260 |
Resumo: | In this work we analyze the version of Hilbert’s 16th problem for piecewise linear differential systems in the plane for a particular case, more precisely in Chapter 2 we study on the maximum numbers of crossing limit cycles that can have the planar piecewise linear differential systems separated by a straight line S and formed by two linear differential systems X−;X+ which singularities are symmetrical with respect to the straight line of discontinuity S and they are on the straight line y = sx, s e R. In [24, 27] it was proved that piecewise linear differential centers separated by a straight line have no crossing limit cycles nevertheless in [20, 28] were studied planar discontinuous piecewise linear differential centers where the curve of discontinuity is not a straight line, and it was shown that the number of crossing limit cycles in these systems is non-zero. For this reason it is interesting to study the role which plays the shape of the discontinuity curve in the number of crossing limit cycles that planar discontinuous piecewise linear differential centers can have. In Chapter 3 we study on the upper bounds for the maximum number of crossing limit cycles with either two or four points on the discontinuity curve S, when S is any conic. And finally in Chapter 4 we study on the numbers of crossing limit cycles with four points on the discontinuity curve S, when S is a reducible cubic curve formed either by a circle and a straight line, or by a parabola and a straight line. |
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Medrado, João Carlos da Rochahttp://lattes.cnpq.br/5021927574622286Saló, Jaume LlibreMedrado, João Carlos da RochaTonon, Durval JoséLima, Maurício Firmino SilvaMartins, Ricardo MirandaBuzzi, Cláudio Aguinaldohttp://lattes.cnpq.br/6731543668602292Ruiz, Jeidy Johana Jimenez2019-12-30T15:33:18Z2019-12-05RUIZ, Jeidy Johana Jimenez. On the crossing limit cycles for piecewise linear differential systems on the plane. 2019. 162 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2019.http://repositorio.bc.ufg.br/tede/handle/tede/10260ark:/38995/001300000f4fmIn this work we analyze the version of Hilbert’s 16th problem for piecewise linear differential systems in the plane for a particular case, more precisely in Chapter 2 we study on the maximum numbers of crossing limit cycles that can have the planar piecewise linear differential systems separated by a straight line S and formed by two linear differential systems X−;X+ which singularities are symmetrical with respect to the straight line of discontinuity S and they are on the straight line y = sx, s e R. In [24, 27] it was proved that piecewise linear differential centers separated by a straight line have no crossing limit cycles nevertheless in [20, 28] were studied planar discontinuous piecewise linear differential centers where the curve of discontinuity is not a straight line, and it was shown that the number of crossing limit cycles in these systems is non-zero. For this reason it is interesting to study the role which plays the shape of the discontinuity curve in the number of crossing limit cycles that planar discontinuous piecewise linear differential centers can have. In Chapter 3 we study on the upper bounds for the maximum number of crossing limit cycles with either two or four points on the discontinuity curve S, when S is any conic. And finally in Chapter 4 we study on the numbers of crossing limit cycles with four points on the discontinuity curve S, when S is a reducible cubic curve formed either by a circle and a straight line, or by a parabola and a straight line.Neste trabalho estudamos a versão do 16th problema de Hilbert para sistemas suaves por partes para um caso particular, mais precisamente no Capítulo 2 estudamos sobre o número máximo de ciclos que podem ter os sistemas lineares por partes separados por uma linha reta S e formados por dois sistemas lineares diferenciais X−;X+ cujas singularidades são simétricas com relação à linha de descontinuidade S e estão sobre a linha reta y = sx, s e R. Em [24, 27] foi provado que os sistemas lineares suaves po partes formados por centros lineares separados por uma linha reta não têm ciclos limite costurantes no entanto em [20, 28] foram estudados estes mesmos sistemas quando a curva de descontinuidade não é uma linha reta e foi mostrado que o número de ciclos limite costurantes nesses sistemas é diferente de zero. Por esta razão é interesante estudar a influência da curva de descontinuidade no número de ciclos limite costurantes que sistemas suaves por partes formados por centros lineares podem possuir. No Capítulo 3 estudamos sobre as cotas superiores para o número máximo de ciclos limite costurantes com dois ou quatro pontos sobre a curva de descontinuidade S, quando S é uma cônica qualquer. Finalmente no Capítulo 4 estudamos sobre o número de ciclos limite costurantes com quatro pontos sobre a curva de descontinuidade S, quando S é uma cúbica redutível formada por um círculo e uma linha reta ou por uma parábola e uma linha reta.Submitted by Onia Arantes Albuquerque (onia.ufg@gmail.com) on 2019-12-26T13:42:21Z No. of bitstreams: 2 Tese - Jeidy Johana Jimenez Ruiz - 2019.pdf: 4926767 bytes, checksum: d6c000423a987fb8307fd6f68d85764f (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2019-12-30T15:33:18Z (GMT) No. of bitstreams: 2 Tese - Jeidy Johana Jimenez Ruiz - 2019.pdf: 4926767 bytes, checksum: d6c000423a987fb8307fd6f68d85764f (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Made available in DSpace on 2019-12-30T15:33:18Z (GMT). No. of bitstreams: 2 Tese - Jeidy Johana Jimenez Ruiz - 2019.pdf: 4926767 bytes, checksum: d6c000423a987fb8307fd6f68d85764f (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2019-12-05Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/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/openAccessPiecewise linear differential systemsCrossing limit cyclesLinear differential centersConicsCubicSistemas diferencias suaves por partesCiclos limite costurantesCentros diferencias linearesCônicasCúbicasCIENCIAS EXATAS E DA TERRA::MATEMATICAOn the crossing limit cycles for piecewise linear differential systems on the planeSobre os ciclos limite costurantes para sistemas lineares por partes no planoinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis6600717948137941247600600600600-4268777512335152015-70908234179844016942075167498588264571reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGORIGINALTese - Jeidy Johana Jimenez Ruiz - 2019.pdfTese - Jeidy Johana Jimenez Ruiz - 2019.pdfapplication/pdf4926767http://repositorio.bc.ufg.br/tede/bitstreams/2872d714-5a9e-4ba8-b92f-b3bfa11dccd2/downloadd6c000423a987fb8307fd6f68d85764fMD55LICENSElicense.txtlicense.txttext/plain; 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dc.title.eng.fl_str_mv |
On the crossing limit cycles for piecewise linear differential systems on the plane |
dc.title.alternative.por.fl_str_mv |
Sobre os ciclos limite costurantes para sistemas lineares por partes no plano |
title |
On the crossing limit cycles for piecewise linear differential systems on the plane |
spellingShingle |
On the crossing limit cycles for piecewise linear differential systems on the plane Ruiz, Jeidy Johana Jimenez Piecewise linear differential systems Crossing limit cycles Linear differential centers Conics Cubic Sistemas diferencias suaves por partes Ciclos limite costurantes Centros diferencias lineares Cônicas Cúbicas CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
On the crossing limit cycles for piecewise linear differential systems on the plane |
title_full |
On the crossing limit cycles for piecewise linear differential systems on the plane |
title_fullStr |
On the crossing limit cycles for piecewise linear differential systems on the plane |
title_full_unstemmed |
On the crossing limit cycles for piecewise linear differential systems on the plane |
title_sort |
On the crossing limit cycles for piecewise linear differential systems on the plane |
author |
Ruiz, Jeidy Johana Jimenez |
author_facet |
Ruiz, Jeidy Johana Jimenez |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Medrado, João Carlos da Rocha |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/5021927574622286 |
dc.contributor.advisor-co1.fl_str_mv |
Saló, Jaume Llibre |
dc.contributor.referee1.fl_str_mv |
Medrado, João Carlos da Rocha |
dc.contributor.referee2.fl_str_mv |
Tonon, Durval José |
dc.contributor.referee3.fl_str_mv |
Lima, Maurício Firmino Silva |
dc.contributor.referee4.fl_str_mv |
Martins, Ricardo Miranda |
dc.contributor.referee5.fl_str_mv |
Buzzi, Cláudio Aguinaldo |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/6731543668602292 |
dc.contributor.author.fl_str_mv |
Ruiz, Jeidy Johana Jimenez |
contributor_str_mv |
Medrado, João Carlos da Rocha Saló, Jaume Llibre Medrado, João Carlos da Rocha Tonon, Durval José Lima, Maurício Firmino Silva Martins, Ricardo Miranda Buzzi, Cláudio Aguinaldo |
dc.subject.eng.fl_str_mv |
Piecewise linear differential systems Crossing limit cycles Linear differential centers Conics Cubic |
topic |
Piecewise linear differential systems Crossing limit cycles Linear differential centers Conics Cubic Sistemas diferencias suaves por partes Ciclos limite costurantes Centros diferencias lineares Cônicas Cúbicas CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.por.fl_str_mv |
Sistemas diferencias suaves por partes Ciclos limite costurantes Centros diferencias lineares Cônicas Cúbicas |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
In this work we analyze the version of Hilbert’s 16th problem for piecewise linear differential systems in the plane for a particular case, more precisely in Chapter 2 we study on the maximum numbers of crossing limit cycles that can have the planar piecewise linear differential systems separated by a straight line S and formed by two linear differential systems X−;X+ which singularities are symmetrical with respect to the straight line of discontinuity S and they are on the straight line y = sx, s e R. In [24, 27] it was proved that piecewise linear differential centers separated by a straight line have no crossing limit cycles nevertheless in [20, 28] were studied planar discontinuous piecewise linear differential centers where the curve of discontinuity is not a straight line, and it was shown that the number of crossing limit cycles in these systems is non-zero. For this reason it is interesting to study the role which plays the shape of the discontinuity curve in the number of crossing limit cycles that planar discontinuous piecewise linear differential centers can have. In Chapter 3 we study on the upper bounds for the maximum number of crossing limit cycles with either two or four points on the discontinuity curve S, when S is any conic. And finally in Chapter 4 we study on the numbers of crossing limit cycles with four points on the discontinuity curve S, when S is a reducible cubic curve formed either by a circle and a straight line, or by a parabola and a straight line. |
publishDate |
2019 |
dc.date.accessioned.fl_str_mv |
2019-12-30T15:33:18Z |
dc.date.issued.fl_str_mv |
2019-12-05 |
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.citation.fl_str_mv |
RUIZ, Jeidy Johana Jimenez. On the crossing limit cycles for piecewise linear differential systems on the plane. 2019. 162 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2019. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/10260 |
dc.identifier.dark.fl_str_mv |
ark:/38995/001300000f4fm |
identifier_str_mv |
RUIZ, Jeidy Johana Jimenez. On the crossing limit cycles for piecewise linear differential systems on the plane. 2019. 162 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2019. ark:/38995/001300000f4fm |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/10260 |
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eng |
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eng |
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6600717948137941247 |
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600 600 600 600 |
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dc.relation.cnpq.fl_str_mv |
-7090823417984401694 |
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2075167498588264571 |
dc.rights.driver.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
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Universidade Federal de Goiás |
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Programa de Pós-graduação em Matemática (IME) |
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UFG |
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Brasil |
dc.publisher.department.fl_str_mv |
Instituto de Matemática e Estatística - IME (RG) |
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Universidade Federal de Goiás |
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