{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T17:24:15Z","timestamp":1648661055435},"reference-count":26,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2013,6]]},"abstract":"<jats:p> 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. <\/jats:p>","DOI":"10.1142\/s021812741330019x","type":"journal-article","created":{"date-parts":[[2013,7,9]],"date-time":"2013-07-09T22:22:13Z","timestamp":1373408533000},"page":"1330019","source":"Crossref","is-referenced-by-count":0,"title":["THE 2-D SEXTIC HAMILTONIAN OSCILLATOR"],"prefix":"10.1142","volume":"23","author":[{"given":"F. 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