An uniparametric 4-DOF Hamiltonian family of perturbed oscillators in 1:1:1:1
resonance is studied. The model includes some classical cases, in particular Zeeman
and the van der Waals systems. First several invariant manifolds are identified.
Normalization by Lie-transforms (only first order is considered here) as well as geometric
reduction related to the invariants associated to the symmetries is used, based
on previous work of the authors. More precisely we find that crossing two of the
integrable cases, B = 1/2 and 1, the family undergoes degenerate Hopf bifurcations,
which at first order shows up as a center-cusp bifurcation. Higher order normalization
and singularity analysis is needed, in order to fully describe the dynamics
around those integrable cases.
|Title of host publication||Actas de las XI Jornadas de Mecánica Celeste (Ezcaray, Spain, June 25-27, 2008)|
|Editors||V. Lanchares, A. Elipe|
|Place of Publication||Zaragoza|
|Publisher||Real Academia de Ciencias de Zaragoza|
|Publication status||Published - 2009|
|Name||Monografías de la Real Academia de Ciencias de Zaragoza|