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dc.creatorPalacián Subiela, Jesús Franciscoes_ES
dc.creatorVidal Díaz, Claudioes_ES
dc.creatorVidarte, Jhones_ES
dc.creatorYanguas Sayas, Patriciaes_ES
dc.identifier.issn0951-7715 (Print)
dc.identifier.issn1361-6544 (Electronic)
dc.descriptionThis is a peer-reviewed, un-copyedited version of an article published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at
dc.description.abstractA family of perturbed Hamiltonians H = 1/2 (x^2 + X^2) − 1/2 (y^2 + Y^2)+1/2 (z^2 + Z^2) + 2[ (x^4 + y^4 + z^4) + (x^2 y^2 + x^2 z^2 + y^2 z^2)] in 1: −1:1 resonance depending on two real parameters is considered. We show the existence and stability of periodic solutions using reduction and averaging. In fact, there are at most thirteen families for every energy level h < 0 and at most twenty six families for every h > 0. The different types of periodic solutions for every nonzero energy level, as well as their bifurcations, are characterised in terms of the parameters. The linear stability of each family of periodic solutions, together with the determination of KAM 3-tori encasing some of the linearly stable periodic solutions is proved. Critical Hamiltonian bifurcations on the reduced space are characterised. We find important differences with respect to the dynamics of the 1:1:1 resonance with the same perturbation as the one given here. We end up with an intuitive interpretation of the results from a cosmological viewpoint.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 Science, Innovation and Universities of Spain. C Vidal is partially supported by Project Fondecyt 1180288.en
dc.format.extent37 p.
dc.publisherIOP Publishingen
dc.relation.ispartofNonlinearity 32 3406en
dc.rights© 2019 IOP Publishing Ltd & London Mathematical Societyen
dc.subjectResonant Hamiltoniansen
dc.subjectFriedmann–Lemaître–Robertson–Walker modelen
dc.subjectNormalisation and reductionen
dc.subjectHamiltonian Hopf bifurcationen
dc.subjectKAM torien
dc.subjectCosmological Hamiltonianen
dc.subjectReduced space and invariantsen
dc.titlePeriodic solutions, KAM tori and bifurcations in a cosmology-inspired potentialen
dc.typeArtículo / Artikuluaes
dc.contributor.departmentEstadística, Informática y Matemáticases_ES
dc.contributor.departmentEstatistika, Informatika eta Matematikaeu
dc.contributor.departmentInstitute for Advanced Materials and Mathematics - INAMAT2es_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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