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.
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We thank M. V. Karasev for helpful discussions. This research was partially supported by CONA-CYT under grant no. 55463.