On the Accuracy of Persistence of Adiabatic Invariant in Single-frequency Systems

A modified method of A.A. Slutskin (1963) of analytical extension to the complex time plane of solutions of a single-frequency nonlinear Hamiltonian system with slowly varying parameters is considered. On the basis of this method a proof of the estimate for the accuracy of persistence of adiabatic invariant due to A.A. Slutskin is given for such systems.