Convergence versus integrability in Birkhoff normal form

2001/04/29 by Nguyen Tien Zung, Zung, Nguyen Tien
Mathematics · #70HXX #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DS #math.SG #msc:70HXX

paper · pdf · doi:10.48550/arxiv.math/0104279

final version, slightly improved presentation

arxiv created 2003/12/04 · arxiv updated 2009/11/30

Abstract

We 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.

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