Existence of divergent Birkhoff normal forms of Hamiltonian functions

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dc.creatorGong, Xianghong
dc.date2003-07-29
dc.date.accessioned2026-07-07T04:59:57Z
dc.date.available2026-07-07T04:59:57Z
dc.descriptionWe 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.
dc.description7 pages
dc.identifierhttps://arxiv.org/abs/math/0307379
dc.identifierhttp://arxiv.org/abs/math/0307379
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68200
dc.subjectDynamical Systems
dc.subject37J40
dc.titleExistence of divergent Birkhoff normal forms of Hamiltonian functions
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