 2118 Rafael de la Llave, Maria Saprykina
 Convergence of the Birkhoff normal form sometimes
implies
convergence of
a normalizing transformation
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Mar 24, 21

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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
nondegenerate quadratic
part. We prove that in this case there is an analytic canonical
transformationnot just a formal power seriesbringing
the Hamiltonian into its Birkhoff normal form.
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