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

Abstract

Differential-geometric properties of the Hamiltonian connections on symplectic manifolds for the adiabatically perturbed Hamiltonian system are studied. Namely, the associated Hamiltonian connection on the main foliation is constructed and its description is given in terms of covariant derivatives and the curvature form of the corresponding connection.