Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systems

In this paper we completely characterize trivial isochronous centers of degrees 5 and 7. Precisely, we provide formulas, up to linear change of coordinates, for the Hamiltonian H of the isochronous centers such that H =(f_1^2 f_2^2)/2 has degrees 6 and 8, and f = (f_1, f_2): R^2 R^2 is a polynomial...

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Autores: Braun, Francisco|||0000-0003-3594-9809, Llibre, Jaume|||0000-0002-9511-5999, Mereu, Ana Cristina
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:169474
Acceso en línea:https://ddd.uab.cat/record/169474
https://dx.doi.org/urn:doi:10.3934/dcds.2016029
Access Level:acceso abierto
Palabra clave:Isochronous centers
Jacobian conjecture
Polynomial Hamiltonian systems
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spelling Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systemsBraun, Francisco|||0000-0003-3594-9809Llibre, Jaume|||0000-0002-9511-5999Mereu, Ana CristinaIsochronous centersJacobian conjecturePolynomial Hamiltonian systemsIn this paper we completely characterize trivial isochronous centers of degrees 5 and 7. Precisely, we provide formulas, up to linear change of coordinates, for the Hamiltonian H of the isochronous centers such that H =(f_1^2 f_2^2)/2 has degrees 6 and 8, and f = (f_1, f_2): R^2 R^2 is a polynomial map with D f = 1 and f(0,0) = (0,0). 22016-01-0120162016-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/169474https://dx.doi.org/urn:doi:10.3934/dcds.2016029reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-40998-PAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-568European Commission https://doi.org/10.13039/501100000780 316338European Commission https://doi.org/10.13039/501100000780 316339open accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1694742026-06-06T12:50:31Z
dc.title.none.fl_str_mv Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systems
title Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systems
spellingShingle Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systems
Braun, Francisco|||0000-0003-3594-9809
Isochronous centers
Jacobian conjecture
Polynomial Hamiltonian systems
title_short Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systems
title_full Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systems
title_fullStr Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systems
title_full_unstemmed Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systems
title_sort Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systems
dc.creator.none.fl_str_mv Braun, Francisco|||0000-0003-3594-9809
Llibre, Jaume|||0000-0002-9511-5999
Mereu, Ana Cristina
author Braun, Francisco|||0000-0003-3594-9809
author_facet Braun, Francisco|||0000-0003-3594-9809
Llibre, Jaume|||0000-0002-9511-5999
Mereu, Ana Cristina
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
Mereu, Ana Cristina
author2_role author
author
dc.subject.none.fl_str_mv Isochronous centers
Jacobian conjecture
Polynomial Hamiltonian systems
topic Isochronous centers
Jacobian conjecture
Polynomial Hamiltonian systems
description In this paper we completely characterize trivial isochronous centers of degrees 5 and 7. Precisely, we provide formulas, up to linear change of coordinates, for the Hamiltonian H of the isochronous centers such that H =(f_1^2 f_2^2)/2 has degrees 6 and 8, and f = (f_1, f_2): R^2 R^2 is a polynomial map with D f = 1 and f(0,0) = (0,0).
publishDate 2016
dc.date.none.fl_str_mv 2
2016-01-01
2016
2016-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/169474
https://dx.doi.org/urn:doi:10.3934/dcds.2016029
url https://ddd.uab.cat/record/169474
https://dx.doi.org/urn:doi:10.3934/dcds.2016029
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-40998-P
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-568
European Commission https://doi.org/10.13039/501100000780 316338
European Commission https://doi.org/10.13039/501100000780 316339
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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