(Springer Nature, 1997) Ferrer, S.; Viartola, A.; Palacián Subiela, Jesús Francisco; Yanguas Sayas, Patricia; San Juan Díaz, Juan Félix; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza; Institute for Advanced Materials and Mathematics - INAMAT2; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
In this Note we study perturbed isotropic harmonic oscillators in 1-
1-1 resonance, which is one of the typical cases of galactic potential models. We
focus on cubic and quartic axial symmetric potentials giving explicitly their normal
form. The 3D normalized Hénon and Heiles case, which requires to reach fourth
order, is studied showing its relative equilibria and bifurcations.