Poisson maps and integrable deformations of Kowalevski top

Abstract

We construct a Poisson map between manifolds with linear Poisson brackets corresponding to the Lie algebras $e(3)$ and $so(4)$. Using this map we establish a connection between the deformed Kowalevski top on $e(3)$ proposed by Sokolov and the Kowalevski top on $so(4)$. The connection between these systems leads to the separation of variables for the deformed system on $e(3)$ and yields the natural $5\times 5$ Lax pair for the Kowalevski top on $so(4)$.

19 pages, Latex with AMS fonts

References in corpus (1)

• On the Lax pairs for the generalized Kowalewski and Goryachev-Chaplygin tops

Cited by in corpus (18)

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• On integrable system on $S^2$ with the second integral quartic in the momenta
• On integration of the Kowalevski gyrostat and the Clebsch problems
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• The group theoretical description of the three-body problem
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• Deformations of the Poisson brackets and the Kowalevski top
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• On Classical r-Matrix for the Kowalevski Gyrostat on so(4)
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• Classical R-matrices for generalized so(p,q) tops
• Phase topology of the Kowalevski-Sokolov top