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Poisson maps and integrable deformations of Kowalevski top

I. V. Komarov·V. V. Sokolov·A. V. Tsiganov
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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 $so(4)$.

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I. V. Komarov, V. V. Sokolov, A. V. Tsiganov. 2003-04-16. Poisson maps and integrable deformations of Kowalevski top. https://doi.org/10.1088/0305-4470%2F36%2F29%2F309

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