Mel’nikov-Samoilenko adiabatic stability problem - Prykarpatsky, Ya. A. (Ukrains’kyi Matematychnyi Zhurnal, 2006)
We develop a symplectic method for the investigation of invariant submanifolds of nonautonomous Hamiltonian systems and ergodic measures on them. The so-called Mel’nikov-Samoilenko problem for the case of adiabatically perturbed completely integrable oscillator-type Hamiltonian systems is studied on the basis of a new construction of “ virtual” canonical transformations.