@inproceedings{1de7ab0d8d2c46bf91aca0c1c46e1671,
title = "Generalized Van der Waals 4-D oscillator. Invariant tori and relative equilibria in Ξ = L = 0 surface",
abstract = "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.",
author = "G. D{\'i}az and J. Egea and S. Ferrer and {Meer, van der}, J.C. and J.A. Vera",
year = "2009",
language = "English",
series = "Monograf{\'i}as de la Real Academia de Ciencias de Zaragoza",
publisher = "Real Academia de Ciencias de Zaragoza",
pages = "19--37",
editor = "V. Lanchares and A. Elipe",
booktitle = "Actas de las XI Jornadas de Mec{\'a}nica Celeste (Ezcaray, Spain, June 25-27, 2008)",
}