Palacián Subiela, Jesús FranciscoVidal Díaz, ClaudioVidarte, JhonYanguas Sayas, Patricia2019-08-282020-08-0520190951-7715 (Print)1361-6544 (Electronic)10.1088/1361-6544/ab1bc6https://academica-e.unavarra.es/handle/2454/34657This 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 https://doi.org/10.1088/1361-6544/ab1bc6.A 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.37 p.application/pdfeng© 2019 IOP Publishing Ltd & London Mathematical SocietyResonant HamiltoniansFriedmann–Lemaître–Robertson–Walker modelNormalisation and reductionHamiltonian Hopf bifurcationKAM toriCosmological HamiltonianReduced space and invariantsArtículo / ArtikuluaAcceso abierto / Sarbide irekiainfo:eu-repo/semantics/openAccess