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dc.creatorCarrasco, Dantees_ES
dc.creatorPalacián Subiela, Jesús Franciscoes_ES
dc.creatorVidal Díaz, Claudioes_ES
dc.creatorVidarte, Jhones_ES
dc.creatorYanguas Sayas, Patriciaes_ES
dc.identifier.issn0938-8974 (Print)
dc.identifier.issn1432-1467 (Electronic)
dc.descriptionThis 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
dc.description.abstractWe 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.en
dc.description.sponsorshipThe 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).en
dc.relation.ispartofJournal of Nonlinear Science (2018) 28:1293–1359en
dc.rights© Springer Science+Business Media, LLC, part of Springer Nature 2018en
dc.subjectSymplectic reductionsen
dc.subjectAxial symmetryen
dc.subjectRelative equilibriaen
dc.subjectPeriodic solutionsen
dc.subjectParametric bifurcationsen
dc.subjectInvariant torien
dc.titleDynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonanceen
dc.typeArtículo / Artikuluaes
dc.contributor.departmentMatematika eta Informatika Ingeniaritzaeu
dc.contributor.departmentInstitute for Advanced Materials and Mathematics - INAMAT2en
dc.contributor.departmentIngeniería Matemática e Informáticaes_ES
dc.rights.accessRightsAcceso abierto / Sarbide irekiaes
dc.relation.projectIDinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-88137-C2-1-P/ES/en
dc.type.versionVersión aceptada / Onetsi den bertsioaes

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