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Caractère Gevrey du développement formel des solutions canard de l’équation de Van der Pol. (Gevrey character of formal expansion of Van der Pol’s equation canard solutions). (French) Zbl 0749.34031

Summary: We prove that formal expansion in the parameter \(\varepsilon\) of Van der Pol’s equation canard solutions is Gevrey 1. Following a suggestion of J. Ecalle, we obtain a way to compute these solutions by using divergent series summation techniques.

MSC:

34E15 Singular perturbations for ordinary differential equations
40G05 Cesàro, Euler, Nörlund and Hausdorff methods
03H05 Nonstandard models in mathematics
26E35 Nonstandard analysis
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