The action-angle coordinates revisited: bi-Hamiltonian systems (Q1573832)
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scientific article; zbMATH DE number 1486461
| Language | Label | Description | Also known as |
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| English | The action-angle coordinates revisited: bi-Hamiltonian systems |
scientific article; zbMATH DE number 1486461 |
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The action-angle coordinates revisited: bi-Hamiltonian systems (English)
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9 August 2000
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A method for using the action-angle variables to construct compatible bi-Hamiltonian structures for completely integrable systems is presented. The main theorem proved states that if the graph of a completely integrable Hamiltonian is a hypersurface of translation with respect to the action variables and each frequency depends only on a single action, then a master symmetry which transforms the system into a bi-Hamiltonian form is constructed. This result is applied to the Kepler problem and many invariant quantities are derived.
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bi-Hamiltonian systems
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action-angle variables
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