Higher Orders of Perturbation Theory in Classical Mechanics

It is known that perturbation theory in classical mechanics, in general, is asymptotic, i.e., the nth coefficient of the corresponding series grows rapidly as n approaches infinity. For certain problems, it is interesting to know the explicit behavior of this coefficient at large n. The general method of the asymptotic calculation of large orders of perturbation series in classical mechanics proposed by Bogomol'nyi (1983) is discussed. The results of the calculation of large orders of perturbations for two-dimensional area-preserving mappings and for the Henon-Heiles model that is defined by a Hamiltonian with two degrees of freedom are presented.