Bohlin-Arnold-Vassiliev's duality and conserved quantities

Bohlin-Arnold-Vassiliev’s duality transformation establishes a correspondence between motions in different central potentials. It offers a very direct way to construct the dynamical conserved quantities associated to the isotropic harmonic oscillator (Fradkin-Jauch-Hill tensor) and to the Kepler’s problem (Laplace-Runge-Lenz vector).