Mel’nikov-Samoilenko adiabatic stability problem
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.
English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 6, pp 887-903.
Citation Example: Prykarpatsky Ya. A. Mel’nikov-Samoilenko adiabatic stability problem // Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 787–803.