poisson commuting polynomials and integrable hamiltonians

We shortly review the concepts of integrable and superintegrable hamiltonians. we then describea dynamics obtained by performing a remarkable non-linear transformation on free motion. theequations obtained in this way, the so-called goldsh' equations, must therefore be derivable from ahamiltonian. we provide such a hamiltonian and show that it is in fact superintegrable by explicitlydisplaying an appropriate number of integrals of motion.