Geodesic
Convergence or generic divergence of the Birkhoff normal form
Ricardo Pérez-Marco1
1 Department of Mathematics, UCLA, Los Angeles, CA 90095, United States and Départament de Mathématiques, Universit$eacute; Paris-Sud, F-91405 Orsay, France
Annals of mathematics, Tome 157 (2003) no. 2, pp. 557-574.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove that the Birkhoff normal form of hamiltonian flows at a nonresonant singular point with given quadratic part is always convergent or generically divergent. The same result is proved for the normalization mapping and any formal first integral.
DOI : 10.4007/annals.2003.157.557

Ricardo Pérez-Marco 1

1 Department of Mathematics, UCLA, Los Angeles, CA 90095, United States and Départament de Mathématiques, Universit$eacute; Paris-Sud, F-91405 Orsay, France 
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Ricardo Pérez-Marco. Convergence or generic divergence of the Birkhoff normal form. Annals of mathematics, Tome 157 (2003) no. 2, pp. 557-574. doi : 10.4007/annals.2003.157.557. http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.157.557/

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