On the global structure of normal forms for slow-fast Hamiltonian systems

Abstract

In the framework of Lie transforms and the global method of averaging, the normal forms of a multidimensional slow-fast Hamiltonian system are studied in the case when the flow of the unperturbed (fast) system is periodic and the induced \(\mathbb{S}^1 \)1-action is not necessarily free and trivial. An intrinsic splitting of the second term in a \(\mathbb{S}^1 \)1-invariant normal form of first order is derived in terms of the Hannay-Berry connection assigned to the periodic flow.