Newton-Hooke type symmetry of anisotropic oscillators

Abstract

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.

Updated version with more figures added. 34 pages, 7 figures. Dedicated to the memory of J.-M. Souriau, deceased on March 15 2012, at the age of 90

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