Rafael de la Llave, Maria Saprykina
Convergence of the Birkhoff normal form sometimes 
implies 
convergence of 
a normalizing transformation
(474K, PDF)

ABSTRACT.  onsider an analytic Hamiltonian system near its analytic invariant 
torus $\mathcal T_0$ carrying zero frequency. 
We assume that the Birkhoff normal form of the Hamiltonian at 
$\mathcal T_0$ is convergent and 
has a particular form: it is an analytic function of its 
non-degenerate quadratic 
part. We prove that in this case there is an analytic canonical 
transformation---not just a formal power series---bringing 
the Hamiltonian into its Birkhoff normal form.