Change of the time for the periodic Toda lattices and natural systems on the plane with higher order integrals of motion |
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Authors: | A. V. Tsiganov |
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Affiliation: | 1. St. Petersburg State University Petrodvorets, Ulyanovskaya str. 1, St. Petersburg, 198504, Russia
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Abstract: | We discuss some special classes of canonical transformations of the time variable, which relate different integrable systems. Such dual systems have different integrals of motion, Lax equations, separated variables and bi-hamiltonian structures. As an example the two-dimensional periodic Toda lattices associated with the classical root systems and the dual natural systems on the palne are considered in detail. |
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