Homological Equation for Tensor Field and Periodic Averaging

Abstract

Homological equations of tensor type associated to periodic flows on a manifold are studied. The Cushman intrinsic formula is generalized to the case of multivector fields and differential forms. Some applications to normal forms and the averaging method for perturbed Hamiltonian systems on slow-fast phase spaces are given.

Cited by in corpus (4)

• Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems
• Kato perturbation expansion in classical mechanics and an explicit expression for a Deprit generator
• A simple global representation for second-order normal forms of Hamiltonian systems relative to periodic flows
• A geometric proof of the periodic averaging theorem on Riemannian manifolds