On a Strange Resonance Noticed by M.Herman

    2001, Volume 6, Number 4, pp.  421-432

    Author(s): Abdullah K., Albouy A.

    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.
    Citation: Abdullah K., Albouy A., On a Strange Resonance Noticed by M.Herman, Regular and Chaotic Dynamics, 2001, Volume 6, Number 4, pp. 421-432

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