Periodic solutions for nonlinear differential systems: the second order bifurcation function

We are concerned here with the classical problem of Poincaré of persistence of periodic solutions under small perturbations. The main contribution of this work is to give the expression of the second order bifurcation function in more general hypotheses than the ones already existing in the literatu...

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Authors: Buica, Adriana, Giné, Jaume, Llibre, Jaume
Format: article
Status:Versión enviada para evaluación y publicación
Publication Date:2014
Country:España
Institution:Universitat de Lleida (UdL)
Repository:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/60382
Online Access:http://hdl.handle.net/10459.1/60382
Access Level:Open access
Keyword:Periodic solution
Lyapunov-Schmidt reduction
Period manifold
Small parameter
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spelling Periodic solutions for nonlinear differential systems: the second order bifurcation functionBuica, AdrianaGiné, JaumeLlibre, JaumePeriodic solutionLyapunov-Schmidt reductionPeriod manifoldSmall parameterWe are concerned here with the classical problem of Poincaré of persistence of periodic solutions under small perturbations. The main contribution of this work is to give the expression of the second order bifurcation function in more general hypotheses than the ones already existing in the literature. We illustrate our main result constructing a second order bifurcation function for the perturbed symmetric Euler top.The first and second authors are partially supported by the MICINN/FEDER grant number MTM2011-22877 and by a AGAUR (Generalitat de Catalunya) grant number 2009SGR–381. The first author was also partially supported by a grant of the Romanian National Authority for Scientific Research, CNCS UEFISCDI, project number PN-II-ID-PCE-2011-3-0094. The third author is partially supported by the MICINN/FEDER grant MTM2008–03437, by AGAUR grant number 2009SGR–410 and ICREA Academia.Nicolaus Copernicus University in Torun, Juliusz Schauder Centre for Nonlinear Studies2014info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionhttp://hdl.handle.net/10459.1/60382reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)InglésMICINN/PN2008-2011/MTM2011-22877MICINN/PN2008-2011/MTM2008-03437Versió preprint del document publicat a http://apcz.umk.pl/czasopisma/index.php/TMNA/article/view/TMNA.2014.024Topological Methods in Nonlinear Analysis, 2014, vol. 43, núm. 2, p. 403-419(c) Nicolaus Copernicus University in Torun, Juliusz Schauder Centre for Nonlinear Studies, 2014info:eu-repo/semantics/openAccessoai:repositori.udl.cat:10459.1/603822026-06-24T12:42:17Z
dc.title.none.fl_str_mv Periodic solutions for nonlinear differential systems: the second order bifurcation function
title Periodic solutions for nonlinear differential systems: the second order bifurcation function
spellingShingle Periodic solutions for nonlinear differential systems: the second order bifurcation function
Buica, Adriana
Periodic solution
Lyapunov-Schmidt reduction
Period manifold
Small parameter
title_short Periodic solutions for nonlinear differential systems: the second order bifurcation function
title_full Periodic solutions for nonlinear differential systems: the second order bifurcation function
title_fullStr Periodic solutions for nonlinear differential systems: the second order bifurcation function
title_full_unstemmed Periodic solutions for nonlinear differential systems: the second order bifurcation function
title_sort Periodic solutions for nonlinear differential systems: the second order bifurcation function
dc.creator.none.fl_str_mv Buica, Adriana
Giné, Jaume
Llibre, Jaume
author Buica, Adriana
author_facet Buica, Adriana
Giné, Jaume
Llibre, Jaume
author_role author
author2 Giné, Jaume
Llibre, Jaume
author2_role author
author
dc.subject.none.fl_str_mv Periodic solution
Lyapunov-Schmidt reduction
Period manifold
Small parameter
topic Periodic solution
Lyapunov-Schmidt reduction
Period manifold
Small parameter
description We are concerned here with the classical problem of Poincaré of persistence of periodic solutions under small perturbations. The main contribution of this work is to give the expression of the second order bifurcation function in more general hypotheses than the ones already existing in the literature. We illustrate our main result constructing a second order bifurcation function for the perturbed symmetric Euler top.
publishDate 2014
dc.date.none.fl_str_mv 2014
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10459.1/60382
url http://hdl.handle.net/10459.1/60382
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv MICINN/PN2008-2011/MTM2011-22877
MICINN/PN2008-2011/MTM2008-03437
Versió preprint del document publicat a http://apcz.umk.pl/czasopisma/index.php/TMNA/article/view/TMNA.2014.024
Topological Methods in Nonlinear Analysis, 2014, vol. 43, núm. 2, p. 403-419
dc.rights.none.fl_str_mv (c) Nicolaus Copernicus University in Torun, Juliusz Schauder Centre for Nonlinear Studies, 2014
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Nicolaus Copernicus University in Torun, Juliusz Schauder Centre for Nonlinear Studies, 2014
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Nicolaus Copernicus University in Torun, Juliusz Schauder Centre for Nonlinear Studies
publisher.none.fl_str_mv Nicolaus Copernicus University in Torun, Juliusz Schauder Centre for Nonlinear Studies
dc.source.none.fl_str_mv reponame:Repositori Obert UdL
instname:Universitat de Lleida (UdL)
instname_str Universitat de Lleida (UdL)
reponame_str Repositori Obert UdL
collection Repositori Obert UdL
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.81155

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