# Exponential stability in the perturbed central force problem

## TL;DR

This paper proves exponential stability for perturbed central force systems with analytic potentials, excluding Keplerian and Harmonic cases, using Nekhoroshev's theorem, and extends results to systems interacting with slow dynamics.

## Contribution

It establishes nondegeneracy conditions for all analytic potentials except Keplerian and Harmonic, enabling exponential stability results via Nekhoroshev's theorem.

## Key findings

- Exponential stability holds for most analytic potentials.
- Stability over long times is proven for systems interacting with slow dynamics.
- Keplerian and Harmonic potentials are exceptions to the stability results.

## Abstract

We consider the spatial central force problem with a real analytic potential. We prove that for all analytic potentials, but 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 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.