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

PHYSICA D-NONLINEAR PHENOMENA

卷:239

Article

Diaz, G.²  Egea, J.²  Ferrer, S.²  van der Meer, J. C.¹  Vera, J. A.³ 

[1] Tech Univ Eindhoven, Fac Wiskunde & Informat, NL-5600 MB Eindhoven, Netherlands

[2] Univ Murcia, Dept Matemat Aplicada, Espinardo 30071, Spain

[3] Univ Politecn Cartagena, Dept Matemat Aplicada & Estadist, Cartagena 30203, Spain

关键词: Nonlinear Hamiltonian system;    Bifurcation;    Reduction;    Symmetry;    Hamiltonian-Hopf bifurcation;    van der Waals system;   

DOI  :  10.1016/j.physd.2010.04.012

来源: Elsevier

【 摘 要 】

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 the previous work of the authors. A description is given for the lower dimensional relative equilibria in such normalized systems for which we introduce, in this context, the new concept of moment polytope. In addition bifurcations of relative equilibria corresponding to 3D tori are studied in some particular cases where we focus on Hamiltonian-Hopf bifurcations and bifurcations in the 3D van der Waals and Zeeman systems. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

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