Abstract
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 correspondingr-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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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 1, pp. 72–94, July, 2000.
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Tsyganov, A.V. Canonical transformations of the extended phase space and integrable systems. Theor Math Phys 124, 918–937 (2000). https://doi.org/10.1007/BF02551068
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DOI: https://doi.org/10.1007/BF02551068