Geodesic
Canonical transformations of the extended phase space and integrable systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 1, pp. 72-94

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We investigate the explicit construction of a canonical transformation of the time variable and the Hamiltonian whereby a given completely integrable system is mapped into another integrable system. The change of time induces a transformation of the equations of motion and of their solutions, the integrals of motion, the methods of separation of variables, the Lax matrices, and the corresponding $r$-matrices. For several specific families of integrable systems (Toda chains, Holt systems, and Stäckel-type systems), we construct canonical transformations of time in the extended phase space that preserve the integrability property. 
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     author = {A. V. Tsiganov},
     title = {Canonical transformations of the extended phase space and integrable systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
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     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_124_1_a5/}
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A. V. Tsiganov. Canonical transformations of the extended phase space and integrable systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 1, pp. 72-94. http://geodesic.mathdoc.fr/item/TMF_2000_124_1_a5/