A New Method for Establishing the Existence of Analytic Functions. Iii. Generic Stability of Hamiltonian Systems

摘要

It is proved that near a singular point or a periodic solution of a Hamiltonian system with an arbitrary number of degrees of freedom the system is stable for almost all the cases if it is stable in the first approximation. This stability is established in the following strong sense: Near the singular point or periodic solution the entire neighborhood is filled in a smooth way with families of concentric periodic surfaces. The results are for analytic systems only. (Author)