21-18 Rafael de la Llave, Maria Saprykina

Convergence of the Birkhoff normal form sometimes implies convergence of a normalizing transformation (474K, PDF) 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 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.

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