Completely integrable bi-Hamiltonian systems (Q1319925)
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scientific article; zbMATH DE number 553852
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Completely integrable bi-Hamiltonian systems |
scientific article; zbMATH DE number 553852 |
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Completely integrable bi-Hamiltonian systems (English)
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19 April 1994
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The author proves that a completely integrable Hamiltonian system is bi- Hamiltonian if and only if the graph of the Hamiltonian function is a hypersurface of translation relative to the affine structure defined by the action variables. This theorem allows to construct a whole hierarchy of the first integrals for such a type of Hamiltonians by means of a recursion method due to F. Magri (1978).
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completely integrable Hamiltonian system
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bi-Hamiltonian
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