Homological Equation for Tensor Field and Periodic Averaging

TL;DR

This paper studies homological equations for tensor fields related to periodic flows, generalizes Cushman's formula to multivector fields and forms, and applies these results to normal forms and averaging in perturbed Hamiltonian systems.

Contribution

It extends Cushman's intrinsic formula to tensor fields and demonstrates applications in normal forms and averaging methods for Hamiltonian systems.

Findings

Generalized Cushman's formula to multivector fields and differential forms.

Provided new methods for normal forms in dynamical systems.

Applied results to averaging in perturbed Hamiltonian systems.

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.