Ciclos limite para a equação de Abel generalizada
Autor(a) principal: | |
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Data de Publicação: | 2009 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tde/2883 |
Resumo: | In this work we conducted a study on the equations of the type dx dt = nå i=0 ai(t)xi; (A) where ai 2 C1, i = 0; ;n and 0 t 1. An equation of the form (A) is called a generalized Abel equation. Our study refers to the problem proposed by C. Pugh: There is a natural number N depending only on n, such that the equation (A) has at most N limit cycles? Initially we study the problem of C. Pugh for n = 1 and n = 2, for which the equation (A) has at most one and two limit cycles, respectively. For n = 3, A. Lins Neto shows that if a3(t) does not change sign on [0;1], then the equation (A) has at most three limit cycles. Also A. Lins Neto shows that, given a natural number l, it is possible to construct an equation of the form (A) with n = 3 that has at least l limit cycles. Still for n = 3, A. Gasull and J. Llibre study the problem of C. Pugh considering that a2(t) does not change sign on [0;1], and M. J. Alvarez, A. Gasull and H. Giacomini also study the problem of C. Pugh considering that there are real numbers a and b such that aa3(t)+ba2(t) does not change sign on [0;1] and a1(t) = a0(t) = 0. Besides this, we study some more general results studied by A. Gasull and A. Guillamon. |
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Garcia, Ronaldo Alveshttp://lattes.cnpq.br/5680428710939826http://lattes.cnpq.br/0039531856534989Belisário, Hugo Leonardo da Silva2014-08-06T10:24:20Z2009-10-30BELISÁRIO, Hugo Leonardo da Silva. Ciclos limite para a equação de Abel generalizada. 2009. 39 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2009.http://repositorio.bc.ufg.br/tede/handle/tde/2883ark:/38995/00130000064z2In this work we conducted a study on the equations of the type dx dt = nå i=0 ai(t)xi; (A) where ai 2 C1, i = 0; ;n and 0 t 1. An equation of the form (A) is called a generalized Abel equation. Our study refers to the problem proposed by C. Pugh: There is a natural number N depending only on n, such that the equation (A) has at most N limit cycles? Initially we study the problem of C. Pugh for n = 1 and n = 2, for which the equation (A) has at most one and two limit cycles, respectively. For n = 3, A. Lins Neto shows that if a3(t) does not change sign on [0;1], then the equation (A) has at most three limit cycles. Also A. Lins Neto shows that, given a natural number l, it is possible to construct an equation of the form (A) with n = 3 that has at least l limit cycles. Still for n = 3, A. Gasull and J. Llibre study the problem of C. Pugh considering that a2(t) does not change sign on [0;1], and M. J. Alvarez, A. Gasull and H. Giacomini also study the problem of C. Pugh considering that there are real numbers a and b such that aa3(t)+ba2(t) does not change sign on [0;1] and a1(t) = a0(t) = 0. Besides this, we study some more general results studied by A. Gasull and A. Guillamon.Neste trabalho realizamos um estudo sobre as equações do tipo dx dt = nå i=0 ai(t)xi; (A) onde ai 2 C1, i = 0; ;n e 0 t 1. Uma equação da forma (A) é denominada equação de Abel generalizada. Nosso estudo se refere ao problema proposto por C. Pugh: existe um número natural N dependendo apenas de n, tal que a equação (A) possui no máximo N ciclos limites? Inicialmente estudamos o problema de C. Pugh para n=1 e n=2, para os quais a equação (A) possui, no máximo, um e dois ciclos limite, respectivamente. Para n = 3, A. Lins Neto mostra que, se a3(t) não muda de sinal em [0;1], então a equação (A) possui no máximo três ciclos limite. Além disso A. Lins Neto mostra que, dado um número natural l, é possível construir uma equação da forma (A) com n = 3 que possui no mínimo l ciclos limites. Ainda para n = 3, A. Gasull e J. Llibre estudam o problema de C. Pugh considerando que a2(t) não muda de sinal em [0;1], e M. J. Álvarez, A. Gasull e H. Giacomini também estudam o problema de C. Pugh considerando que existem números reais a e b tais que aa3(t)+ba2(t) não muda de sinal em [0;1] e a1(t) = a0(t) = 0. Além destes resultados, estudamos alguns resultados mais gerais estudados por A. Gasull e A. Guillamon.Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2014-08-06T10:24:20Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) ciclos_limites_para_a_equacao_de_abel_generalizada.pdf: 641062 bytes, checksum: e4be39606562d4f6805c21c2cceb451c (MD5)Made available in DSpace on 2014-08-06T10:24:20Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) ciclos_limites_para_a_equacao_de_abel_generalizada.pdf: 641062 bytes, checksum: e4be39606562d4f6805c21c2cceb451c (MD5) Previous issue date: 2009-10-30Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPqapplication/pdfhttp://repositorio.bc.ufg.br/tede/retrieve/6058/ciclos_limites_para_a_equacao_de_abel_generalizada.pdf.jpgporUniversidade Federal de GoiásPrograma de Pós-graduação em Matemática (IME)UFGBrasilInstituto de Matemática e Estatística - IME (RG)[1] GASULL, A; GUILLAMON, A. Limit cicles for generalized Abel equations. International Journal of Bifurcation and Chaos, 16(12):3737–3745, 2006. [2] GASULL, A; LLIBRE, J. Limit cycles for a class of Abel equations. Siam J. Math. Anal, 21(5):1235–1244, 1990. [3] HALE, J. K; KOÇAK, H. Dynamics and Bifurcations. Springer-Verlag, 1991. [4] HOLBOE, B. Oeuvres Complètes de N. H. Abel. Chez Chr Gröndahl, Imprimeur- Libraire, (Volume 2): 229-245, 1839. Disponível on-line: http://books.google. com.br/books?id=yS4VAAAAQAAJ&dq=Oeuvres%20compl%C3%A8tes%20Niels% 20Henrik%20Abel&lr=&pg=RA1-PA229#v=onepage&q=&f=false, Acesso em: 24/09/2009. [5] LINS N., A. On the number of solutions of the equation dx dt =ånj =0 aj(t)x j, 0 t 1, for which x(0) = x(1). Inventiones Matematicae, (59):67–76, 1980. [6] ÁLVAREZ, M. J; GASULL, A; GIACOMINI, H. A new uniqueness criterion for the number of periodic orbits of Abel equations. Journal of Differential Equations, (234):161–176, 2007. [7] PERKO, L. Differencial Equations and Dynamical Systems. Springer-Verlag, 1991. [8] SOTOMAYOR, J. Lições de Equações Diferenciais Ordinárias. Projeto Euclides, IMPA, 1979.6600717948137941247600600600600-4268777512335152015-7090823417984401694-2555911436985713659http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessEquação de AbelAplicação de PoincaréEstabilidade de órbitas periódicasCiclo limite16º problema de HilbertAbel equationPoincaré mapStability of periodic órbitsLimit cycle16th Hilbert problemCIENCIAS EXATAS E DA TERRA::MATEMATICACiclos limite para a equação de Abel generalizadaLimit cycles for generalized Abel equationinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisreponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; charset=utf-82142http://repositorio.bc.ufg.br/tede/bitstreams/a3582cb9-5708-4c94-ad25-dda74b3bd68d/download232e528055260031f4e2af4136033daaMD51CC-LICENSElicense_urllicense_urltext/plain; charset=utf-849http://repositorio.bc.ufg.br/tede/bitstreams/38c2a6a6-8185-44ff-adf5-f8ecf66bc193/download4afdbb8c545fd630ea7db775da747b2fMD52license_textlicense_texttext/html; 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dc.title.por.fl_str_mv |
Ciclos limite para a equação de Abel generalizada |
dc.title.alternative.eng.fl_str_mv |
Limit cycles for generalized Abel equation |
title |
Ciclos limite para a equação de Abel generalizada |
spellingShingle |
Ciclos limite para a equação de Abel generalizada Belisário, Hugo Leonardo da Silva Equação de Abel Aplicação de Poincaré Estabilidade de órbitas periódicas Ciclo limite 16º problema de Hilbert Abel equation Poincaré map Stability of periodic órbits Limit cycle 16th Hilbert problem CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Ciclos limite para a equação de Abel generalizada |
title_full |
Ciclos limite para a equação de Abel generalizada |
title_fullStr |
Ciclos limite para a equação de Abel generalizada |
title_full_unstemmed |
Ciclos limite para a equação de Abel generalizada |
title_sort |
Ciclos limite para a equação de Abel generalizada |
author |
Belisário, Hugo Leonardo da Silva |
author_facet |
Belisário, Hugo Leonardo da Silva |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Garcia, Ronaldo Alves |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/5680428710939826 |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/0039531856534989 |
dc.contributor.author.fl_str_mv |
Belisário, Hugo Leonardo da Silva |
contributor_str_mv |
Garcia, Ronaldo Alves |
dc.subject.por.fl_str_mv |
Equação de Abel Aplicação de Poincaré Estabilidade de órbitas periódicas Ciclo limite 16º problema de Hilbert |
topic |
Equação de Abel Aplicação de Poincaré Estabilidade de órbitas periódicas Ciclo limite 16º problema de Hilbert Abel equation Poincaré map Stability of periodic órbits Limit cycle 16th Hilbert problem CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Abel equation Poincaré map Stability of periodic órbits Limit cycle 16th Hilbert problem |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
In this work we conducted a study on the equations of the type dx dt = nå i=0 ai(t)xi; (A) where ai 2 C1, i = 0; ;n and 0 t 1. An equation of the form (A) is called a generalized Abel equation. Our study refers to the problem proposed by C. Pugh: There is a natural number N depending only on n, such that the equation (A) has at most N limit cycles? Initially we study the problem of C. Pugh for n = 1 and n = 2, for which the equation (A) has at most one and two limit cycles, respectively. For n = 3, A. Lins Neto shows that if a3(t) does not change sign on [0;1], then the equation (A) has at most three limit cycles. Also A. Lins Neto shows that, given a natural number l, it is possible to construct an equation of the form (A) with n = 3 that has at least l limit cycles. Still for n = 3, A. Gasull and J. Llibre study the problem of C. Pugh considering that a2(t) does not change sign on [0;1], and M. J. Alvarez, A. Gasull and H. Giacomini also study the problem of C. Pugh considering that there are real numbers a and b such that aa3(t)+ba2(t) does not change sign on [0;1] and a1(t) = a0(t) = 0. Besides this, we study some more general results studied by A. Gasull and A. Guillamon. |
publishDate |
2009 |
dc.date.issued.fl_str_mv |
2009-10-30 |
dc.date.accessioned.fl_str_mv |
2014-08-06T10:24:20Z |
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 |
dc.identifier.citation.fl_str_mv |
BELISÁRIO, Hugo Leonardo da Silva. Ciclos limite para a equação de Abel generalizada. 2009. 39 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2009. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tde/2883 |
dc.identifier.dark.fl_str_mv |
ark:/38995/00130000064z2 |
identifier_str_mv |
BELISÁRIO, Hugo Leonardo da Silva. Ciclos limite para a equação de Abel generalizada. 2009. 39 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2009. ark:/38995/00130000064z2 |
url |
http://repositorio.bc.ufg.br/tede/handle/tde/2883 |
dc.language.iso.fl_str_mv |
por |
language |
por |
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6600717948137941247 |
dc.relation.confidence.fl_str_mv |
600 600 600 600 |
dc.relation.department.fl_str_mv |
-4268777512335152015 |
dc.relation.cnpq.fl_str_mv |
-7090823417984401694 |
dc.relation.sponsorship.fl_str_mv |
-2555911436985713659 |
dc.relation.references.por.fl_str_mv |
[1] GASULL, A; GUILLAMON, A. Limit cicles for generalized Abel equations. International Journal of Bifurcation and Chaos, 16(12):3737–3745, 2006. [2] GASULL, A; LLIBRE, J. Limit cycles for a class of Abel equations. Siam J. Math. Anal, 21(5):1235–1244, 1990. [3] HALE, J. K; KOÇAK, H. Dynamics and Bifurcations. Springer-Verlag, 1991. [4] HOLBOE, B. Oeuvres Complètes de N. H. Abel. Chez Chr Gröndahl, Imprimeur- Libraire, (Volume 2): 229-245, 1839. Disponível on-line: http://books.google. com.br/books?id=yS4VAAAAQAAJ&dq=Oeuvres%20compl%C3%A8tes%20Niels% 20Henrik%20Abel&lr=&pg=RA1-PA229#v=onepage&q=&f=false, Acesso em: 24/09/2009. [5] LINS N., A. On the number of solutions of the equation dx dt =ånj =0 aj(t)x j, 0 t 1, for which x(0) = x(1). Inventiones Matematicae, (59):67–76, 1980. [6] ÁLVAREZ, M. J; GASULL, A; GIACOMINI, H. A new uniqueness criterion for the number of periodic orbits of Abel equations. Journal of Differential Equations, (234):161–176, 2007. [7] PERKO, L. Differencial Equations and Dynamical Systems. Springer-Verlag, 1991. [8] SOTOMAYOR, J. Lições de Equações Diferenciais Ordinárias. Projeto Euclides, IMPA, 1979. |
dc.rights.driver.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
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dc.publisher.none.fl_str_mv |
Universidade Federal de Goiás |
dc.publisher.program.fl_str_mv |
Programa de Pós-graduação em Matemática (IME) |
dc.publisher.initials.fl_str_mv |
UFG |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Instituto de Matemática e Estatística - IME (RG) |
publisher.none.fl_str_mv |
Universidade Federal de Goiás |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFG instname:Universidade Federal de Goiás (UFG) instacron:UFG |
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Repositório Institucional da UFG |
bitstream.url.fl_str_mv |
http://repositorio.bc.ufg.br/tede/bitstreams/a3582cb9-5708-4c94-ad25-dda74b3bd68d/download http://repositorio.bc.ufg.br/tede/bitstreams/38c2a6a6-8185-44ff-adf5-f8ecf66bc193/download http://repositorio.bc.ufg.br/tede/bitstreams/11e7ec62-82ff-4e67-8943-1ee01f5a82e2/download http://repositorio.bc.ufg.br/tede/bitstreams/d5d90256-5104-4d2c-9562-47d2057b9898/download http://repositorio.bc.ufg.br/tede/bitstreams/ca948aee-002f-44e9-917c-e2264a51cb04/download http://repositorio.bc.ufg.br/tede/bitstreams/f500df6d-128b-4f4e-892e-c11e62316cd8/download http://repositorio.bc.ufg.br/tede/bitstreams/769af679-67dd-4d6e-98eb-7e4a3fb79381/download |
bitstream.checksum.fl_str_mv |
232e528055260031f4e2af4136033daa 4afdbb8c545fd630ea7db775da747b2f 9833653f73f7853880c94a6fead477b1 9da0b6dfac957114c6a7714714b86306 e4be39606562d4f6805c21c2cceb451c 312a96b3b7419c49469b2d4adc2db6c8 3ae71a8ac8f6b7b5d272a1939c35d93f |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 MD5 MD5 |
repository.name.fl_str_mv |
Repositório Institucional da UFG - Universidade Federal de Goiás (UFG) |
repository.mail.fl_str_mv |
tasesdissertacoes.bc@ufg.br |
_version_ |
1811721411952115712 |