Hamiltonian perturbation theory on a manifold
The author develops a ``global'' formulation of Hamiltonian perturbation theory, in which the normal forms are globally defined on the phase space manifold. The geometry of the fibration by the invariant tori of an integrable degenerate Hamiltonian system does not possess a global system of coordinates of action-angle type which is the key for this study. This degenerate system can be described by some generalizations of the Liouville-Arnold's theorem. As an application a ``global'' formulation of Nekhoroshev's theorem on the stability for exponentially long times is given.
scientific article; zbMATH DE number 798823
scientific article