Existence of divergent Birkhoff normal forms of Hamiltonian functions

Details Existence of divergent Birkhoff normal forms of Hamiltonian functions Existence of divergent Birkhoff normal forms of Hamiltonian functions

2003-07-29

arxiv.org/abs/math/0307379v1

Mathematics

Dynamical Systems

7 pages

Scientific paper

We show that for $n \geq 2$ there exist real analytic Hamiltonian systems on
$\mathbf{R}^{2n}$ with non-resonant eigenvalues at a singular point, of which
the Birkhoff normal form itself is divergent. The proof of the result is
achieved by analyzing how the small-divisors enter the normal form.

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