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.


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