An accelerated elimination technique for the solution of perturbed Hamiltonian systems

Abstract

A new technique is developed for the formal solution of non-degenerate or degenerate Hamiltonian systems under periodic perturbation through continually accelerated elimination of the periodic terms. Special features of the method are the ability to eliminate both short-period and longperiod variables simultaneously and the attainment of [formal] ‘quadratic convergence’ for non-degenerate systems and nearly quadratic convergence in degenerate cases. The technique utilizes Lie transforms and is based on an approach due to Kolmogorov and Arnol'd.