Lie Point Symmetries for Reduced Ermakov Systems
  Reduced Ermakov systems are defined as Ermakov systems restricted to the level surfaces of the Ermakov invariant. The condition for Lie point symmetries for reduced Ermakov systems is solved yielding four infinite families of systems. It is shown that SL(2,R) always is a group of point symmetries for the reduced Ermakov systems. The theory is applied to a model example and to the equations of motion of an ion under a generalized Paul trap. 
F. Haas and J. Goedert