0 Convergence or generic divergence of Birkhoff normal form
نویسنده
چکیده
We prove that Birkhoff normal form of hamiltonian flows at a non-resonant singular point with given quadratic part are always convergent or generically divergent. The same result is proved for the normalization mapping and any formal first integral.
منابع مشابه
Existence of Divergent Birkhoff Normal Forms of Hamiltonian Functions
where κ = 0, . . . , n, and λj is pure imaginary precisely when 1 ≤ j ≤ κ, and λ1, −λ1, . . . , λn, −λn are eigenvalues of Hzz(0)J with z = (x, y) and Jxj = yj = −J yj. One says that λ1, . . . , λn are non-resonant, if λ ·α ≡ λ1α1 + · · ·+λnαn 6= 0 for all multi-indices of integers α 6= 0. The Birkhoff normal form says that under the non-resonance condition on λ, there is a formal symplectic tr...
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تاریخ انتشار 2000