Title: 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.