PERTURBED GYLDEN SYSTEMS AND TIME-DEPENDENT DELAUNAY-LIKE TRANSFORMATIONS

We study the possibilities and limitations of the application of gener alized Delaunay-like transformations (in the 6-dimensional phase space ) and TR-like mappings (in the 8-dimensional, extended phase space) to perturbed two-body problems with a time-varying Keplerian parameter m u(t), that is, to Gylden-type systems. For the sake of theoretical com pleteness, both negative-and positive-energy motion (with nonstationar y coupling parameter) are, in principle, considered. Our developments are intended to introduce canonical variables parallelling the classic al ones of Delaunay and the Delaunay-Similar variables of Scheifele.