Rigorous estimates for the relegation algorithm
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 clas...
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| Veröffentlicht in: | Celestial mechanics and dynamical astronomy 2017, Vol.127 (1), p.1-18 |
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| container_title | Celestial mechanics and dynamical astronomy |
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| creator | Sansottera, Marco Ceccaroni, Marta |
| description | 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. |
| doi_str_mv | 10.1007/s10569-016-9711-2 |
| format | Article |
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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
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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. 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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.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10569-016-9711-2</doi><tpages>18</tpages></addata></record> |
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| subjects | Aerospace Technology and Astronautics Algebra Algorithms Astronomy Astrophysics and Astroparticles Classical Mechanics Convergence Dynamical Systems and Ergodic Theory Estimates Exact solutions Geophysics/Geodesy Mathematical analysis Original Article Perturbation theory Physics Physics and Astronomy Theory Transformations |
| title | Rigorous estimates for the relegation algorithm |
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