Qualitative Investigation of Almost Separable Hamiltonian System of Two Degrees of Freedom

摘要: The present paper is a condensed survey of some qualitative methods to investigate the orbits Hamiltonian dynamical systems. In particular we consider autonomous problems two degrees freedom which are globally almost separable or admit periodic solution (local separability) and can be reduced non-autonomous, system one degree (by isoenergetic reduction). general priori given unperturbed problem not structurally stable at all, an interesting subset phase space (as e g, regions resonance). To deal with this situation propose perform finite perturbation procedure based on averaging principle that defines new larger set than original one. content consists in exploring idea from several points view. Some applications celestial mechanics included. More details will published elsewhere.