Generalized Van der Waals 4-D oscillator. Invariant tori and relative equilibria in Ξ = L = 0 surface

G. Díaz, J. Egea, S. Ferrer, J.C. Meer, van der, J.A. Vera

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267 Citations (Scopus)
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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.
Original languageEnglish
Title of host publicationActas de las XI Jornadas de Mecánica Celeste (Ezcaray, Spain, June 25-27, 2008)
EditorsV. Lanchares, A. Elipe
Place of PublicationZaragoza
PublisherReal Academia de Ciencias de Zaragoza
Pages19-37
Publication statusPublished - 2009

Publication series

NameMonografías de la Real Academia de Ciencias de Zaragoza
Volume32
ISSN (Print)1132-6360

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