On the definition of the Delaunay-similar canonical variables of Scheifele (Q1342154)

For the definition of the Delaunay-similar canonical variables of Scheifele, the Deprit's technique is used. Firstly, a particular class of time-dependent generating functions involving an arbitrary function is introduced. Then, another arbitrary function is considered in the transformation of the independent variable. With an appropriate selection of these functions, the special cases considered earlier by Scheifele, Sigrist, Deprit and others can be recovered.