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arXiv · 2103.13535

Convergence of the Birkhoff normal form sometimes implies convergence of a normalizing transformation

Rafael de la Llave·Maria Saprykina
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Abstract

Consider 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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Rafael de la Llave, Maria Saprykina. 2021-03-25. Convergence of the Birkhoff normal form sometimes implies convergence of a normalizing transformation. https://arxiv.org/abs/2103.13535

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