Notes on a paper by Lutzky on the noncanonical symmetries of Hamiltonian systems: “Noncanonical symmetries and isospectral representations of Hamiltonian systems”

Abstract

We obtain the first integrals Tr(Rk) by using a differential equation of the Lax type of simpler structure than the one obtained in a recent paper. Certain questions raised in this paper on the relation between noncanonical symmetries S and complete integrability are answered. Additional first integrals depending on the derivatives of S of order greater than one are also obtained.