Imbeddings of integral submanifolds and associated adiabatic invariants ofslowly perturbed integrable Hamiltonian systems

A new method is developed for characterizing the evolution of invariant tor i of slowly varying perturbations of completely integrable (in the sense of Liouville-Arnold [1-3]) Hamiltonian systems on cotangent phase spaces. The method is based on Cartan's theory of integral submanifolds, and it provid es an algebro-analytic approach to the investigation of the embedding [4-10 ] of the invariant tori in phase space that can be used to describe the str ucture of quasi-periodic solutions on the tori. In addition, it leads to an adiabatic perturbation theory [3,12,13] of the corresponding Lagrangian as ymptotic submanifolds via the Poincare-Cartan approach [4], a new Poincare- Melnikov type [5,11,14] procedure for determining stability, and fresh insi ghts into the existence problem for adiabatic invariants [2,3] of the Hamil tonian systems under consideration.