Convergence or generic divergence of the Birkhoff normal form

Abstract

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.

Authors

Ricardo Pérez-Marco

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