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Regular and Chaotic Dynamics

, Volume 23, Issue 7–8, pp 821–841 | Cite as

Exponential Stability in the Perturbed Central Force Problem

  • Dario BambusiEmail author
  • Alessandra Fusè
  • Marco Sansottera
Article
  • 2 Downloads

Abstract

We consider the spatial central force problem with a real analytic potential. We prove that for all analytic potentials, but for the Keplerian and the harmonic ones, the Hamiltonian fulfills a nondegeneracy property needed for the applicability of Nekhoroshev’s theorem. We deduce stability of the actions over exponentially long times when the system is subject to an arbitrary analytic perturbation. The case where the central system is put in interaction with a slow system is also studied and stability over exponentially long time is proved.

Keywords

exponential stability Nekhoroshev theory perturbation theory normal form theory central force problem 

MSC2010 numbers

70K45 34C20 37G05 70F15 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • Dario Bambusi
    • 1
    Email author
  • Alessandra Fusè
    • 1
  • Marco Sansottera
    • 1
  1. 1.Dipartimento di Matematica “Federigo Enriques”Università degli Studi di MilanoMilanoRussia

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