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Keplerization of Bounded Motion in Central Force Fields

A geometric reformulation and generalization of the Martinusi-Gurfil 'keplerization' method, which maps any bounded one-body motion in a spherically symmetric force field onto an equivalent Keplerian orbit. Recast as a general 'homogenization' method for arbitrary bounded motion, it yields a constructive proof of the existence of a dynamical symmetry group for any such system and shows how that group extends to a global symmetry group.