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Regular and Chaotic Dynamics, 1998, Volume 3, Issue 3, Pages 107–121
DOI: https://doi.org/10.1070/RD1998v003n03ABEH000084 (Mi rcd952) 		 
This article is cited in 12 scientific papers (total in 12 papers)

On the 70th birthday of J.Moser

Construction of stable periodic orbits for the spin-orbit problem of celestial mechanics

A. Cellettia, L. Chierchiab

a Dipartimento di Matematica Pura, e Applicata, Universita di L'Aquila, Via Vetoio-I-67010 L'Aquila. Italy
b Dipartimento di Matematica, Universita Roma Tre, Largo San Leonardo Murialdo 1, I-00146 Roma. Italy
Citations (12)
DOI: https://doi.org/10.1070/RD1998v003n03ABEH000084
Abstract: Birkhoff periodic orbits associated to spin-orbit resonances in Celestial Mechanics and in particular to the Moon–Earth and Mercury–Sun systems are considered. A general method (based on a quantitative version of the Implicit Function Theorem) for the construction of such orbits with particular attention to "effective estimates" on the size of the perturbative parameters is presented and tested on the above mentioned systems. Lyapunov stability of the periodic orbits (for small values of the perturbative parameters) is proved by constructing KAM librational invariant surfaces trapping the periodic orbits.
Received: 02.09.1998
Bibliographic databases:
Document Type: Article
MSC: 58F10, 58F22, 70F15
Language: English
Citation: A. Celletti, L. Chierchia, “Construction of stable periodic orbits for the spin-orbit problem of celestial mechanics”, Regul. Chaotic Dyn., 3:3 (1998), 107–121
Citation in format AMSBIB
\Bibitem{CelChi98}
\by A.~Celletti, L. Chierchia
\paper Construction of stable periodic orbits for the spin-orbit problem of celestial mechanics
\jour Regul. Chaotic Dyn.
\yr 1998
\vol 3
\issue 3
\pages 107--121
\mathnet{http://mi.mathnet.ru/rcd952}
\crossref{https://doi.org/10.1070/RD1998v003n03ABEH000084}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1704973}
\zmath{https://zbmath.org/?q=an:0988.37098}
Linking options:
  • https://www.mathnet.ru/eng/rcd952
  • https://www.mathnet.ru/eng/rcd/v3/i3/p107
    • This publication is cited in the following 12 articles:
    1. Xiaodan Xu, Wen Si, Jianguo Si, “The p : q resonance for dissipative spin–orbit problem in celestial mechanics”, Z. Angew. Math. Phys., 75:6 (2024)  crossref
    2. Gabriella Pinzari, Xiang Liu, “Quantitative kam Theory, with an Application to the Three-Body Problem”, J Nonlinear Sci, 33:5 (2023)  crossref
    3. Alessandra Celletti, Encyclopedia of Complexity and Systems Science, 2023, 1  crossref
    4. Alessandra Celletti, Encyclopedia of Complexity and Systems Science Series, Perturbation Theory, 2022, 339  crossref
    5. Alessandra Celletti, Encyclopedia of Complexity and Systems Science, 2022, 1  crossref
    6. Chen Q., Pinzari G., “Exponential Stability of Fast Driven Systems, With An Application to Celestial Mechanics”, Nonlinear Anal.-Theory Methods Appl., 208 (2021), 112306  crossref  mathscinet  isi  scopus
    7. Alessandra Celletti, Mathematics of Complexity and Dynamical Systems, 2012, 1301  crossref
    8. Alessandra Celletti, Sara Di Ruzza, “Periodic and quasi–periodic orbits of the dissipative standard map”, Discrete & Continuous Dynamical Systems - B, 16:1 (2011), 151  crossref
    9. Luigi Chierchia, Gabriella Pinzari, “The planetary N-body problem: symplectic foliation, reductions and invariant tori”, Invent. math., 186:1 (2011), 1  crossref
    10. Alessandra Celletti, Encyclopedia of Complexity and Systems Science, 2009, 6673  crossref
    11. Renato Calleja, Rafael de la Llave, “Fast numerical computation of quasi-periodic equilibrium states in 1D statistical mechanics, including twist maps”, Nonlinearity, 22:6 (2009), 1311  crossref
    12. A. Celletti, “Periodic and Quasi-periodic Attractors of Weakly-dissipative Nearly-integrable Systems”, Regul. Chaotic Dyn., 14:1 (2009), 49–63  mathnet  crossref
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