199034, 7-9, Universitetskaya nab.
Saint-Petersburg State University
Vershilov A. V., Grigoryev Y. A., Tsiganov A. V.
On an integrable deformation of the Kowalevski top
2014, Vol. 10, No. 2, pp. 223-236
We discuss an application of the Poisson brackets deformation theory to the construction of the integrable perturbations of the given integrable systems. The main examples are the known integrable perturbations of the Kowalevski top for which we get new bi-Hamiltonian structures in the framework of the deformation theory.
Vershilov A. V., Tsiganov A. V.
On the Darboux-Nijenhuis Variables on the Poisson Manifold $so^*(4)$
2007, Vol. 3, No. 2, pp. 141-155
We classify quadratic Poisson structures on $so^*(4)$ and $e^*(3)$, which have the same foliations by symplectic leaves as canonical Lie-Poisson tensors. The separated variables for some of the corresponding bi-integrable systems are constructed