On the co-existence of maximal and whiskered tori in the planetary three-body problem

In this paper we discuss about the possibility of {it coexistence} of stable and unstable quasi--periodic {sc kam} tori in a region of phase space of the three-body problem. The {argument of proof} goes along {{sc kam} theory and, especially,} the production of two non smoothly related systems of canonical coordinates in the same region of the phase space, the possibility of which is foreseen, for ``properly--degenerate' systems, by a theorem of Nekhorossev and Mi{{s}}{{c}}enko and Fomenko. The two coordinate systems are alternative to the classical reduction of the nodes by Jacobi, described, e.g., in~Ref.cite[III,S 5, n. 4, p. 141]{arnold63}.