The completeness of some Hamiltonian vector fields on a Poisson manifold (Q2785688)
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scientific article; zbMATH DE number 981829
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The completeness of some Hamiltonian vector fields on a Poisson manifold |
scientific article; zbMATH DE number 981829 |
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24 April 1997
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Poisson manifolds
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Hamiltonian vector fields
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completeness of vector fields
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The completeness of some Hamiltonian vector fields on a Poisson manifold (English)
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It is proved that if a Hamiltonian \(H\in C^{\infty}\) is proper and bounded below, say \(H \geq 0\), then the corresponding Hamiltonian vector field generates a global flow on a finite-dimensional Poisson manifold. This is a generalisation of \textit{W. B. Gordon}'s result in [Proc. Am. Math. Soc. 26, 329-331 (1970; Zbl 0206.10201)].
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