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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

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.

MSC:

34C25 Periodic solutions to ordinary differential equations
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