Hamiltonian geometric connection associated with adiabatically perturbed Hamiltonian systems and the existence of adiabatic invariants

摘要

We study the differential-geometric properties of Hamiltonian connections on symplectic manifolds for adiabatically perturbed Hamiltonian systems. In particular, an associated Hamiltonian connection is constructed on the principal fibration. Its description is given in terms of covariant derivatives and the curvature form of the corresponding connection.