Poisson maps and integrable deformations of Kowalevski top
Komarov, I. V. ; Sokolov, V. V. ; Tsiganov, A. V.
arXiv, 0304033 / Harvested from arXiv
Text on arXiv
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 $so(4)$.
Publié le : 2003-04-16
Classification:  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  High Energy Physics - Theory,  Mathematical Physics 
@article{0304033,
     author = {Komarov, I. V. and Sokolov, V. V. and Tsiganov, A. V.},
     title = {Poisson maps and integrable deformations of Kowalevski top},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0304033}
}

Komarov, I. V.; Sokolov, V. V.; Tsiganov, A. V. Poisson maps and integrable deformations of Kowalevski top. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0304033/