2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61392We show that any analytically integrable Hamiltonian system near an equilibrium point admits a convergent Birkhoff normalization. The proof is based on a new, geometric approach to the problem.final version, slightly improved presentationDynamical SystemsSymplectic Geometry70HXXConvergence versus integrability in Birkhoff normal formtext