Rigorous estimates for the relegation algorithm

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• 作者：Marco Sansottera ; Marta Ceccaroni
• 关键词：Hamiltonian dynamics ; Lie transformations ; Normal forms methods ; Normalization ; Perturbation theory ; Relegation ; Symbolic algebra
• 刊名：Celestial Mechanics and Dynamical Astronomy
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：127
• 期：1
• 页码：1-18
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Astrophysics and Astroparticles; Dynamical Systems and Ergodic Theory; Aerospace Technology and Astronautics; Geophysics/Geodesy; Classical Mechanics;
• 出版者：Springer Netherlands
• ISSN：1572-9478
• 卷排序：127

文摘

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.