Poisson maps and integrable deformations of the 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 × 5 Lax pair for the Kowalevski top on so(4).
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- July 2003
- DOI:
- 10.1088/0305-4470/36/29/309
- arXiv:
- arXiv:nlin/0304033
- Bibcode:
- 2003JPhA...36.8035K
- Keywords:
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- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- High Energy Physics - Theory;
- Mathematical Physics
- E-Print:
- 19 pages, Latex with AMS fonts