Pages 557-574 from Volume 157 (2003), Issue 2 by Ricardo Pérez-Marco
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.
Received: 1 September 2000
Accepted: 8 March 2002
Published online: March 2003
Department of Mathematics, UCLA, Los Angeles, CA 90095, United States and Départament de Mathématiques, Universit$eacute; Paris-Sud, F-91405 Orsay, France