Convergence or generic divergence of the Birkhoff normal form


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.


Ricardo Pérez-Marco

Department of Mathematics, UCLA, Los Angeles, CA 90095, United States and Départament de Mathématiques, Universit$eacute; Paris-Sud, F-91405 Orsay, France