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Convergence versus integrability in Birkhoff normal form. (English) Zbl 1076.37045

Th main result states: Any real (complex) analytically integrable Hamiltonian system in a neighborhood of an equilibrium point on a symplectic manifold admits a real (complex) convergent Birkhoff normalization at that point.

MSC:

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37G05 Normal forms for dynamical systems
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