Đề tài " Convergence versus integrability in Birkhoff normal form "

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 topic. 1. Introduction Among the fundamental problems concerning analytic (real or complex) Hamiltonian systems near an equilibrium point, one may mention the following two: 1) Convergent Birkhoff. In this paper, by “convergent Birkhoff” we mean a normalization, ., a local analytic symplectic system of coordinates in which the Hamiltonian function will Poisson commute with the semisimple part of its quadratic part. .

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2    25    1    05-08-2021