Lax representation and Poisson geometry of the Kowalevski top (Q2716875)
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scientific article; zbMATH DE number 1599574
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lax representation and Poisson geometry of the Kowalevski top |
scientific article; zbMATH DE number 1599574 |
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Lax representation and Poisson geometry of the Kowalevski top (English)
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10 April 2002
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Dirac reduction
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Lax representation
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Poisson geometry
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Kowalevski top
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Gel'fand-Zakharevich geometry
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Kowalevski gyrostat
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Lenard sequences
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It is shown that deformation of the standard Poisson pencil along a triple of characteristic vector fields is the geometric counterpart of an extension of the nine-dimensional Bobenko, Reyman, Semenov-Tian-Shansky phase space. It is demonstrated that the commuting Hamiltonians of the deformed Poisson pencil coincide with those of the underformed pencil. Gel'fand-Zakharevich geometry of the two-field Kowalevski gyrostat is discussed. It may be represented by a pair of Lenard sequences of length 2.
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