The 2-D sextic Hamiltonian oscillator

F.J. Molero, J.C. Meer, van der, S. Ferrer, F. Céspedes

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The 2-D sextic oscillator is studied as a family of axial symmetric parametric integrable Hamiltonian systems, presenting a bifurcation analysis of the different flows. It includes the "elliptic core" model in 1-D nonlinear oscillators, recently proposed in the literature. We make use of the energy-momentum mapping, which will give us the fundamental fibration of the four-dimensional phase space. Special attention is given to the singular values of the energy-momentum mapping connected with rectilinear and circular orbits. They are related to the saddle-center and pitchfork scenarios with the associated homoclinic and heteroclinic trajectories. We also study how the geometry of the phase space evolves during the transition from the one-dimensional to the two-dimensional model. Within an elliptic function approach, the solutions are given using Legendre elliptic integrals of the first and third kind and the corresponding Jacobi elliptic functions.
Original languageEnglish
Pages (from-to)1330019/1-27
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number6
Publication statusPublished - 2013


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