Relative equilibria and bifurcations in the generalized van der Waals 4-D oscillator

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

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A uniparametric 4-DOF family of perturbed Hamiltonian oscillators in 1:1:1:1 resonance is studied as a generalization for several models for perturbed Keplerian systems. 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. A description is given of the lower dimensional relative equilibria in such normalized systems. In addition bifurcations of relative equilibria corresponding to three dimensional tori are studied in some particular cases where we focus on Hamiltonian Hopf bifurcations and bifurcations in the 3-D van der Waals and Zeeman systems.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages37
Publication statusPublished - 2009

Publication series

ISSN (Print)0926-4507


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