ИСТИНА

We show that, in contrast to non-degenerate singular orbits (of elliptic, hyperbolic and focus-focus types), there exist parabolic orbits which are locally fibrewise diffeomorphic, but not symplectomorphic. Furthermore, all symplectic invariants of parabolic orbits (with a given resonance) can be expressed in terms of action variables. Finally, we show that the only symplectic semi-local invariant of a cuspidal torus (with a given resonance) is the canonical integer affine structure on the base of the corresponding singular Lagrangian fibration. In other words, cuspidal tori satisfy a general principle holding for many non-degenerate singular fibres (Delzant 1988; Dufour, Molino and Toulet 1994; Dullin and Vu Ngoc 2007; Vu Ngoc 2003).