Abstract
We consider prenormal forms associated to generic perturbations of the system x ̇ =2y, y ̇ =3x 2 . It is known that they have a formal normal form x ̇ =2y+2x Δ ∗, y ̇ =3x 2+3y Δ ∗ , where Δ ∗=x+A 0(y 2−x 3) [Differential Equations 158 (1) (1999) 152–173]. We show that the series A 0 and the normalizing transformations are divergent, but 1-summable. To cite this article: M. Canalis-Durand, R. Schäfke, C. R. Acad. Sci. Paris, Ser. I 336 (2003).
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