Rigorous estimates for the relegation algorithm

Abstract

We revisit the relegation algorithm by Deprit et al. (Celest. Mech. Dyn. Astron. 79:157-182, 2001) in the light of the rigorous Nekhoroshev's like theory. This relatively recent algorithm is nowadays widely used for implementing closed form analytic perturbation theories, as it generalises the classical Birkhoff normalisation algorithm. The algorithm, here briefly explained by means of Lie transformations, has been so far introduced and used in a formal way, i.e. without providing any rigorous convergence or asymptotic estimates. The overall aim of this paper is to find such quantitative estimates and to show how the results about stability over exponentially long times can be recovered in a simple and effective way, at least in the non-resonant case.

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Cited by in corpus (5)

• A new radial, natural, higher order intermediary of the main problem four decades after the elimination of the parallax
• Closed form perturbation theory in the restricted three-body problem without relegation
• On the continuation of degenerate periodic orbits via normal form: lower dimensional resonant tori
• On the continuation of degenerate periodic orbits via normal form: full dimensional resonant tori
• Relegation-free closed-form perturbation theory and the domain of secular motions in the Restricted 3-Body Problem