On a Strange Resonance Noticed by M.Herman

The linearized averaged system is a classical integrable approximation for a system of n planets. It presents a strange kind of degeneracy that we call "Herman's resonance". The unexpected identity in the expansion of the perturbating function that causes this degeneracy is shown to be part of a family of similar identities. We give a simple Lemma putting together these identities. We also give a precise construction of the averaged system, that allows us to discuss its intrinsic character.