Periodic orbits for a class of reversible quadratic vector field on R-3
Main Author: | |
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Publication Date: | 2007 |
Other Authors: | , |
Format: | Article |
Language: | eng |
Source: | Repositório Institucional da UNESP |
Download full: | http://dx.doi.org/10.1016/j.jmaa.2007.02.011 http://hdl.handle.net/11449/33824 |
Summary: | For a class of reversible quadratic vector fields on R-3 we study the periodic orbits that bifurcate from a heteroclinic loop having two singular points at infinity connected by an invariant straight line in the finite part and another straight line at infinity in the local chart U-2. More specifically, we prove that for all n is an element of N, there exists epsilon(n) > 0 such that the reversible quadratic polynomial differential systemx = a(0) + a(1y) + a(3y)(2) + a(4Y)(2) + epsilon(a(2x)(2) + a(3xz)),y = b(1z) + b(3yz) + epsilon b(2xy),z = c(1y) +c(4az)(2) + epsilon c(2xz)in R-3, with a(0) < 0, b(1)c(1) < 0, a(2) < 0, b(2) < a(2), a(4) > 0, c(2) < a(2) and b(3) is not an element of (c(4), 4c(4)), for epsilon is an element of (0, epsilon(n)) has at least n periodic orbits near the heteroclinic loop. (c) 2007 Elsevier B.V. All rights reserved. |
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Periodic orbits for a class of reversible quadratic vector field on R-3Periodic orbitsQuadratic vector fieldsReversibilityFor a class of reversible quadratic vector fields on R-3 we study the periodic orbits that bifurcate from a heteroclinic loop having two singular points at infinity connected by an invariant straight line in the finite part and another straight line at infinity in the local chart U-2. More specifically, we prove that for all n is an element of N, there exists epsilon(n) > 0 such that the reversible quadratic polynomial differential systemx = a(0) + a(1y) + a(3y)(2) + a(4Y)(2) + epsilon(a(2x)(2) + a(3xz)),y = b(1z) + b(3yz) + epsilon b(2xy),z = c(1y) +c(4az)(2) + epsilon c(2xz)in R-3, with a(0) < 0, b(1)c(1) < 0, a(2) < 0, b(2) < a(2), a(4) > 0, c(2) < a(2) and b(3) is not an element of (c(4), 4c(4)), for epsilon is an element of (0, epsilon(n)) has at least n periodic orbits near the heteroclinic loop. (c) 2007 Elsevier B.V. All rights reserved.Departamento de Matemática, Instituto de Biociências, Letras e Ciências Exatas (IBILCE), Universidade Estadual Paulista (UNESP), São José do Rio Preto, SP, BrasilDepartamento de Matemática, Universidade Autônoma de Barcelona, Barcelona, EspanhaInstituto de Matemática e Estatística, Universidade Federal de Goiás (UFG), Goiânia, GO, BrasilDepartamento de Matemática, Instituto de Biociências, Letras e Ciências Exatas (IBILCE), Universidade Estadual Paulista (UNESP), São José do Rio Preto, SP, BrasilElsevier B. V.Universidade Estadual Paulista (Unesp)Universidade Autônoma de Barcelona (UAB)Universidade Federal de Goiás (UFG)Buzzi, Claudio Aguinaldo [UNESP]Llibre, JaumeMedrado, João Carlos da Rocha2014-05-20T15:22:56Z2014-05-20T15:22:56Z2007-11-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1335-1346application/pdfhttp://dx.doi.org/10.1016/j.jmaa.2007.02.011Journal of Mathematical Analysis and Applications. San Diego: Academic Press Inc. Elsevier B. V., v. 335, n. 2, p. 1335-1346, 2007.0022-247Xhttp://hdl.handle.net/11449/3382410.1016/j.jmaa.2007.02.011WOS:000248854000042WOS000248854000042.pdf66828677607174450000-0003-2037-8417Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Mathematical Analysis and Applications1.138info:eu-repo/semantics/openAccess2023-12-28T06:20:28Zoai:repositorio.unesp.br:11449/33824Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-12-28T06:20:28Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Periodic orbits for a class of reversible quadratic vector field on R-3 |
title |
Periodic orbits for a class of reversible quadratic vector field on R-3 |
spellingShingle |
Periodic orbits for a class of reversible quadratic vector field on R-3 Buzzi, Claudio Aguinaldo [UNESP] Periodic orbits Quadratic vector fields Reversibility |
title_short |
Periodic orbits for a class of reversible quadratic vector field on R-3 |
title_full |
Periodic orbits for a class of reversible quadratic vector field on R-3 |
title_fullStr |
Periodic orbits for a class of reversible quadratic vector field on R-3 |
title_full_unstemmed |
Periodic orbits for a class of reversible quadratic vector field on R-3 |
title_sort |
Periodic orbits for a class of reversible quadratic vector field on R-3 |
author |
Buzzi, Claudio Aguinaldo [UNESP] |
author_facet |
Buzzi, Claudio Aguinaldo [UNESP] Llibre, Jaume Medrado, João Carlos da Rocha |
author_role |
author |
author2 |
Llibre, Jaume Medrado, João Carlos da Rocha |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Universidade Autônoma de Barcelona (UAB) Universidade Federal de Goiás (UFG) |
dc.contributor.author.fl_str_mv |
Buzzi, Claudio Aguinaldo [UNESP] Llibre, Jaume Medrado, João Carlos da Rocha |
dc.subject.por.fl_str_mv |
Periodic orbits Quadratic vector fields Reversibility |
topic |
Periodic orbits Quadratic vector fields Reversibility |
description |
For a class of reversible quadratic vector fields on R-3 we study the periodic orbits that bifurcate from a heteroclinic loop having two singular points at infinity connected by an invariant straight line in the finite part and another straight line at infinity in the local chart U-2. More specifically, we prove that for all n is an element of N, there exists epsilon(n) > 0 such that the reversible quadratic polynomial differential systemx = a(0) + a(1y) + a(3y)(2) + a(4Y)(2) + epsilon(a(2x)(2) + a(3xz)),y = b(1z) + b(3yz) + epsilon b(2xy),z = c(1y) +c(4az)(2) + epsilon c(2xz)in R-3, with a(0) < 0, b(1)c(1) < 0, a(2) < 0, b(2) < a(2), a(4) > 0, c(2) < a(2) and b(3) is not an element of (c(4), 4c(4)), for epsilon is an element of (0, epsilon(n)) has at least n periodic orbits near the heteroclinic loop. (c) 2007 Elsevier B.V. All rights reserved. |
publishDate |
2007 |
dc.date.none.fl_str_mv |
2007-11-15 2014-05-20T15:22:56Z 2014-05-20T15:22:56Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1016/j.jmaa.2007.02.011 Journal of Mathematical Analysis and Applications. San Diego: Academic Press Inc. Elsevier B. V., v. 335, n. 2, p. 1335-1346, 2007. 0022-247X http://hdl.handle.net/11449/33824 10.1016/j.jmaa.2007.02.011 WOS:000248854000042 WOS000248854000042.pdf 6682867760717445 0000-0003-2037-8417 |
url |
http://dx.doi.org/10.1016/j.jmaa.2007.02.011 http://hdl.handle.net/11449/33824 |
identifier_str_mv |
Journal of Mathematical Analysis and Applications. San Diego: Academic Press Inc. Elsevier B. V., v. 335, n. 2, p. 1335-1346, 2007. 0022-247X 10.1016/j.jmaa.2007.02.011 WOS:000248854000042 WOS000248854000042.pdf 6682867760717445 0000-0003-2037-8417 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal of Mathematical Analysis and Applications 1.138 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
1335-1346 application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier B. V. |
publisher.none.fl_str_mv |
Elsevier B. V. |
dc.source.none.fl_str_mv |
Web of Science reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
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1797790134936010752 |