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

2021/03/25 by de la Llave, Rafael, Saprykina, Maria · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2103.13535

Abstract

Consider an analytic Hamiltonian system near its analytic invariant torus \mathcal T₀ carrying zero frequency. We assume that the Birkhoff normal form of the Hamiltonian at \mathcal T₀ 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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