Geodesic
A family of integrable systems on a sphere
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 17, Tome 291 (2002), pp. 263-277

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We discuss some construction of non-canonical transformations connecting different integrable systems on the Poisson manifold. All the considered maps consist of canonical transformations of symplectic leaves and parallel translations induced by diffeomorphisms in the base of symplectic foliation. 
@article{ZNSL_2002_291_a15,
     author = {A. V. Tsiganov},
     title = {A family of integrable systems on a sphere},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {263--277},
     publisher = {mathdoc},
     volume = {291},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_291_a15/}
}
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A. V. Tsiganov. A family of integrable systems on a sphere. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 17, Tome 291 (2002), pp. 263-277. http://geodesic.mathdoc.fr/item/ZNSL_2002_291_a15/