Chenciner, Alain; Gasull, Armengol; Llibre, Jaume Une description compléte du portrait de phase d’un modèle d’élimination résonante. (The phase portrait of a model of resonant elimination). (French) Zbl 0647.34042 C. R. Acad. Sci., Paris, Sér. I 305, 623-626 (1987). Summary: We describe, for every value of the parameters (\(\alpha\),\(\beta)\), the phase portrait of the family of differential equations E(\(\alpha\),\(\beta)\) \[ d\theta /dt=y,\quad dy/dt=\alpha +\beta y+\gamma y^ 2+\delta \cos (2\pi \theta), \] \((\gamma <0\) and \(\delta >0\) fixed). This family plays an important role in the resonant elimination of couples of invariant curves of plane diffeomorphisms. Cited in 4 Documents MSC: 34C25 Periodic solutions to ordinary differential equations Keywords:phase portrait; resonant elimination; invariant curves of plane diffeomorphisms PDFBibTeX XMLCite \textit{A. Chenciner} et al., C. R. Acad. Sci., Paris, Sér. I 305, 623--626 (1987; Zbl 0647.34042)