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Convergence or generic divergence of Birkhoff normal form

Ricardo Perez-Marco
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Abstract

We prove that Birkhoff normal form of hamiltonian flows at a non-resonant singular point with given quadratic part are always convergent or generically divergent. The same result is proved for the normalization mapping and any formal first integral.

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Ricardo Perez-Marco. 2000-09-04. Convergence or generic divergence of Birkhoff normal form. https://arxiv.org/abs/math/0009028

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