# Exponential Stability in the Perturbed Central Force Problem

*2018, Volume 23, Numbers 7-8, pp. 821-841*

Author(s):

**Bambusi D., Fusè A., Sansottera M.**

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 Nekhoroshevâ€™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.

Access to the full text on the Springer website |