Alexander Vershilov

    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.
    Keywords: Poisson geometry, Kowalevski top
    Citation: Vershilov A. V., Grigoryev Y. A., Tsiganov A. V.,  On an integrable deformation of the Kowalevski top, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 2, pp.  223-236
    Vershilov A. V., Tsiganov A. V.
    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
    Keywords: integrable system, bi-hamiltonian geometry, separation of variables
    Citation: Vershilov A. V., Tsiganov A. V.,  On the Darboux-Nijenhuis Variables on the Poisson Manifold $so^*(4)$, Rus. J. Nonlin. Dyn., 2007, Vol. 3, No. 2, pp.  141-155

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