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Invariant Tori in the Secular Motions of the Three-Body Planetary Systems

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New Developments in the Dynamics of Planetary Systems

Abstract

We consider the problem of the applicability of KAM theorem to a realistic problem of three bodies. In the framework of the averaged dynamics over the fast angles for the Sun—Jupiter—Saturn system we can prove the perpetual stability of the orbit. The proof is based on semi-numerical algorithms requiring both explicit algebraic manipulations of series and analytical estimates. The proof is made rigorous by using interval arithmetics in order to control the numerical errors.

In memory of Michèle Moons

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Via Saldini 50, 20133, Milano, Italy

    Ugo Locatelli

  2. Dipartimento di Matematica e Applicazioni, Via degli Arcimboldi 8, 20126, Milano, Italy

    Antonio Giorgilli

Authors
  1. Ugo Locatelli
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  2. Antonio Giorgilli
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Editor information

Editors and Affiliations

  1. Unversity of Vienna, Austria

    Rudolf Dvorak

  2. University of Namur (FUNDP), Belgium

    Jacques Henrard

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© 2001 Springer Science+Business Media Dordrecht

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Locatelli, U., Giorgilli, A. (2001). Invariant Tori in the Secular Motions of the Three-Body Planetary Systems. In: Dvorak, R., Henrard, J. (eds) New Developments in the Dynamics of Planetary Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2414-2_3

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  • DOI: https://doi.org/10.1007/978-94-017-2414-2_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5702-0

  • Online ISBN: 978-94-017-2414-2

  • eBook Packages: Springer Book Archive

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