Dynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonance

This is a post-peer-review, pre-copyedit version of an article published in Journal of Nonlinear Science (2018) 28:1293–1359. The final authenticated version is available online at https://doi.org/10.1007/s00332-018-9449-y

Detalhes bibliográficos
Autores: Carrasco, Dante, Palacián Subiela, Jesús Francisco, Vidal Díaz, Claudio, Vidarte, Jhon, Yanguas Sayas, Patricia
Tipo de documento: artigo
Estado:Versión aceptada para publicación
Data de publicação:2018
País:España
Recursos:Universidad Pública de Navarra
Repositório:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/29051
Acesso em linha:https://hdl.handle.net/2454/29051
Access Level:Acceso aberto
Palavra-chave:Invariants
Symplectic reductions
Axial symmetry
Relative equilibria
Periodic solutions
Parametric bifurcations
Invariant tori
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spelling Dynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonanceCarrasco, DantePalacián Subiela, Jesús FranciscoVidal Díaz, ClaudioVidarte, JhonYanguas Sayas, PatriciaInvariantsSymplectic reductionsAxial symmetryRelative equilibriaPeriodic solutionsParametric bifurcationsInvariant toriThis is a post-peer-review, pre-copyedit version of an article published in Journal of Nonlinear Science (2018) 28:1293–1359. The final authenticated version is available online at https://doi.org/10.1007/s00332-018-9449-yWe study the dynamics of a family of perturbed three-degree-of-freedom Hamiltonian systems which are in 1:1:1 resonance. The perturbation consists of axially symmetric cubic and quartic arbitrary polynomials. Our analysis is performed by normalisation, reduction and KAM techniques. Firstly, the system is reduced by the axial symmetry, and then, periodic solutions and KAM 3-tori of the full system are determined from the relative equilibria. Next, the oscillator symmetry is extended by normalisation up to terms of degree 4 in rectangular coordinates; after truncation of higher orders and reduction to the orbit space, some relative equilibria are established and periodic solutions and KAM 3-tori of the original system are obtained. As a third step, the reduction in the two symmetries leads to a one-degree-of-freedom system that is completely analysed in the twice reduced space. All the relative equilibria together with the stability and parametric bifurcations are determined. Moreover, the invariant 2-tori (related to the critical points of the twice reduced space), some periodic solutions and the KAM3-tori, all corresponding to the full system, are established. Additionally, the bifurcations of equilibria occurring in the twice reduced space are reconstructed as quasi-periodic bifurcations involving 2-tori and periodic solutions of the full system.The authors are partially supported by Projects MTM 2011-28227-C02-01 of the Ministry of Science and Innovation of Spain, MTM 2014-59433-C2-1-P of the Ministry of Economy and Competitiveness of Spain, and MTM 2017-88137-C2-1-P of the Ministry of Economy, Industry and Competitiveness of Spain. D. Carrasco is also partially supported by Project DIUBB 165708 3/R, Universidad del Bío-Bío, Chile and by FONDECYT Project 1181061, CONICYT (Chile).SpringerMatematika eta Informatika IngeniaritzaInstitute for Advanced Materials and Mathematics - INAMAT2Ingeniería Matemática e Informática2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2454/29051reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad Pública de NavarraInglésinfo:eu-repo/grantAgreement/MICINN//MTM2011-28227-C02-01info:eu-repo/grantAgreement/MINECO//MTM2014-59433-C2-1-Pinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-88137-C2-1-P© Springer Science+Business Media, LLC, part of Springer Nature 2018info:eu-repo/semantics/openAccessoai:academica-e.unavarra.es:2454/290512026-06-17T12:41:47Z
dc.title.none.fl_str_mv Dynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonance
title Dynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonance
spellingShingle Dynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonance
Carrasco, Dante
Invariants
Symplectic reductions
Axial symmetry
Relative equilibria
Periodic solutions
Parametric bifurcations
Invariant tori
title_short Dynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonance
title_full Dynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonance
title_fullStr Dynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonance
title_full_unstemmed Dynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonance
title_sort Dynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonance
dc.creator.none.fl_str_mv Carrasco, Dante
Palacián Subiela, Jesús Francisco
Vidal Díaz, Claudio
Vidarte, Jhon
Yanguas Sayas, Patricia
author Carrasco, Dante
author_facet Carrasco, Dante
Palacián Subiela, Jesús Francisco
Vidal Díaz, Claudio
Vidarte, Jhon
Yanguas Sayas, Patricia
author_role author
author2 Palacián Subiela, Jesús Francisco
Vidal Díaz, Claudio
Vidarte, Jhon
Yanguas Sayas, Patricia
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Matematika eta Informatika Ingeniaritza
Institute for Advanced Materials and Mathematics - INAMAT2
Ingeniería Matemática e Informática
dc.subject.none.fl_str_mv Invariants
Symplectic reductions
Axial symmetry
Relative equilibria
Periodic solutions
Parametric bifurcations
Invariant tori
topic Invariants
Symplectic reductions
Axial symmetry
Relative equilibria
Periodic solutions
Parametric bifurcations
Invariant tori
description This is a post-peer-review, pre-copyedit version of an article published in Journal of Nonlinear Science (2018) 28:1293–1359. The final authenticated version is available online at https://doi.org/10.1007/s00332-018-9449-y
publishDate 2018
dc.date.none.fl_str_mv 2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2454/29051
url https://hdl.handle.net/2454/29051
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MICINN//MTM2011-28227-C02-01
info:eu-repo/grantAgreement/MINECO//MTM2014-59433-C2-1-P
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-88137-C2-1-P
dc.rights.none.fl_str_mv © Springer Science+Business Media, LLC, part of Springer Nature 2018
info:eu-repo/semantics/openAccess
rights_invalid_str_mv © Springer Science+Business Media, LLC, part of Springer Nature 2018
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
instname:Universidad Pública de Navarra
instname_str Universidad Pública de Navarra
reponame_str Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
collection Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
repository.name.fl_str_mv
repository.mail.fl_str_mv
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