Newton-Hooke type symmetry of anisotropic oscillators
  The rotation-less Newton--Hooke - type symmetry found recently in the Hill problem and instrumental for explaining the center-of-mass decomposition is generalized to an arbitrary anisotropic oscillator in the plane. Conversely, the latter system is shown, by the orbit method, to be the most general one with such a symmetry. Full Newton-Hooke symmetry is recovered in the isotropic case. Star escape from a Galaxy is studied as application. 
P. M. Zhang, P. A. Horvathy, K. Andrzejewski, J. Gonera, P. Kosinski
hep-th