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.
Citation:
A. V. Tsiganov, “Change of the time for the periodic Toda lattices and natural systems on the plane with higher order integrals of motion”, Regul. Chaotic Dyn., 14:4-5 (2009), 541–549
\Bibitem{Tsi09}
\by A. V. Tsiganov
\paper Change of the time for the periodic Toda lattices and natural systems on the plane with higher order integrals of motion
\jour Regul. Chaotic Dyn.
\yr 2009
\vol 14
\issue 4-5
\pages 541--549
\mathnet{http://mi.mathnet.ru/rcd998}
\crossref{https://doi.org/10.1134/S1560354709040108}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2551876}
\zmath{https://zbmath.org/?q=an:1229.70062}
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https://www.mathnet.ru/eng/rcd998
https://www.mathnet.ru/eng/rcd/v14/i4/p541
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