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.
Keywords:
Toda lattices, change of time
Citation:
Tsiganov A. V., Change of the time for the periodic Toda lattices and natural systems on the plane with higher order integrals of motion, Regular and Chaotic Dynamics,
2009, Volume 14, Numbers 4-5,
pp. 541-549