Meyer, Kenneth RayPalacián Subiela, Jesús FranciscoYanguas Sayas, Patricia2018-05-092019-05-0820180951-7715 (Print)1361-6544 (Electronic)10.1088/1361-6544/aab591https://academica-e.unavarra.es/handle/2454/28577This is an author-created, un-copyedited version of an article accepted for publication/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/aab591.We investigate the dynamics of resonant Hamiltonians with n degrees of freedom to which we attach a small perturbation. Our study is based on the geometric interpretation of singular reduction theory. The flow of the Hamiltonian vector field is reconstructed from the cross sections corresponding to an approximation of this vector field in an energy surface. This approximate system is also built using normal forms and applying reduction theory obtaining the reduced Hamiltonian that is defined on the orbit space. Generically, the reduction is of singular character and we classify the singularities in the orbit space, getting three different types of singular points. A critical point of the reduced Hamiltonian corresponds to a family of periodic solutions in the full system whose characteristic multipliers are approximated accordingly to the nature of the critical point.application/pdfeng© 2018 IOP Publishing Ltd & London Mathematical SocietyNormal form and resonant HamiltonianSingular reductionCross sectionOrbit space and orbifoldPlateauPeak and ridgeSymplectic coordinates and symplectic smoothingArtículo / ArtikuluaAcceso abierto / Sarbide irekiainfo:eu-repo/semantics/openAccess