Shape and period of limit cycles bifurcating from a class of Hamiltonian period annulus

In this work we are concerned with the problem of shape and period of isolated periodic solutions of perturbed analytic radial Hamiltonian vector fields in the plane. Fran¸coise develop a method to obtain the first non vanishing Poincaré-Pontryagin-Melnikov function. We generalize this technique and...

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Autores: Prohens, Rafel|||0000-0003-1184-6311, Torregrosa, Joan|||0000-0002-2753-1827
Tipo de recurso: artículo
Fecha de publicación:2013
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150633
Acceso en línea:https://ddd.uab.cat/record/150633
https://dx.doi.org/urn:doi:10.1016/j.na.2012.10.017
Access Level:acceso abierto
Palabra clave:Polynomial differential equation
Bifurcation of limit cycles
Shape
Number
Location and period of limit cycles
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spelling Shape and period of limit cycles bifurcating from a class of Hamiltonian period annulusProhens, Rafel|||0000-0003-1184-6311Torregrosa, Joan|||0000-0002-2753-1827Polynomial differential equationBifurcation of limit cyclesShapeNumberLocation and period of limit cyclesIn this work we are concerned with the problem of shape and period of isolated periodic solutions of perturbed analytic radial Hamiltonian vector fields in the plane. Fran¸coise develop a method to obtain the first non vanishing Poincaré-Pontryagin-Melnikov function. We generalize this technique and we apply it to know, up to any order, the shape of the limit cycles bifurcating from the period annulus of the class of radial Hamiltonians. We write any solution, in polar coordinates, as a power series expansion in terms of the small parameter. This expansion is also used to give the period of the bifurcated periodic solutions. We present the concrete expression of the solutions up to third order of perturbation of Hamiltonians of the form H = H(r). Necessary and sufficient conditions that show if a solution is simple or double are also presented. 22013-01-0120132013-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/150633https://dx.doi.org/urn:doi:10.1016/j.na.2012.10.017reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2011-22751Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03437Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-410open 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:1506332026-06-06T12:50:31Z
dc.title.none.fl_str_mv Shape and period of limit cycles bifurcating from a class of Hamiltonian period annulus
title Shape and period of limit cycles bifurcating from a class of Hamiltonian period annulus
spellingShingle Shape and period of limit cycles bifurcating from a class of Hamiltonian period annulus
Prohens, Rafel|||0000-0003-1184-6311
Polynomial differential equation
Bifurcation of limit cycles
Shape
Number
Location and period of limit cycles
title_short Shape and period of limit cycles bifurcating from a class of Hamiltonian period annulus
title_full Shape and period of limit cycles bifurcating from a class of Hamiltonian period annulus
title_fullStr Shape and period of limit cycles bifurcating from a class of Hamiltonian period annulus
title_full_unstemmed Shape and period of limit cycles bifurcating from a class of Hamiltonian period annulus
title_sort Shape and period of limit cycles bifurcating from a class of Hamiltonian period annulus
dc.creator.none.fl_str_mv Prohens, Rafel|||0000-0003-1184-6311
Torregrosa, Joan|||0000-0002-2753-1827
author Prohens, Rafel|||0000-0003-1184-6311
author_facet Prohens, Rafel|||0000-0003-1184-6311
Torregrosa, Joan|||0000-0002-2753-1827
author_role author
author2 Torregrosa, Joan|||0000-0002-2753-1827
author2_role author
dc.subject.none.fl_str_mv Polynomial differential equation
Bifurcation of limit cycles
Shape
Number
Location and period of limit cycles
topic Polynomial differential equation
Bifurcation of limit cycles
Shape
Number
Location and period of limit cycles
description In this work we are concerned with the problem of shape and period of isolated periodic solutions of perturbed analytic radial Hamiltonian vector fields in the plane. Fran¸coise develop a method to obtain the first non vanishing Poincaré-Pontryagin-Melnikov function. We generalize this technique and we apply it to know, up to any order, the shape of the limit cycles bifurcating from the period annulus of the class of radial Hamiltonians. We write any solution, in polar coordinates, as a power series expansion in terms of the small parameter. This expansion is also used to give the period of the bifurcated periodic solutions. We present the concrete expression of the solutions up to third order of perturbation of Hamiltonians of the form H = H(r). Necessary and sufficient conditions that show if a solution is simple or double are also presented.
publishDate 2013
dc.date.none.fl_str_mv 2
2013-01-01
2013
2013-01-01
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/150633
https://dx.doi.org/urn:doi:10.1016/j.na.2012.10.017
url https://ddd.uab.cat/record/150633
https://dx.doi.org/urn:doi:10.1016/j.na.2012.10.017
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2011-22751
Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03437
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-410
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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