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).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
