Deformations of Poisson structures on fibered manifolds and adiabatic slow–fast systems

Abstract

In the context of normal forms, we study a class of slow–fast Hamiltonian systems on general Poisson fiber bundles with symmetry. Our geometric approach is motivated by a link between the deformation theory for Poisson structures on fibered manifolds and the adiabatic perturbation theory. We present some normalization results which are based on the averaging theorem for horizontal 2-cocycles on Poisson fiber bundles.