About the Keplerization of motion in any central force field

The method of keplerization of one-body motion in any central force field, introduced by Martinusi and Gurfil in 2012, is reviewed and reformulated into a general homogenization method which applies to any kind of bounded motion. It is also shown how this extended method provides a proof of the existence of a dynamical symmetry group and how it can be used to extend that group to a global symmetry group, for any such system