# Periodic solutions of a perturbed Kepler problem in the plane: from existence to stability

## TL;DR

This paper proves the existence of elliptic periodic solutions in a perturbed planar Kepler problem with time-periodic perturbations, using symplectic group analysis to establish stability and existence results.

## Contribution

It introduces a novel approach based on local symplectic group description to demonstrate existence and stability of periodic solutions in a perturbed Kepler problem.

## Key findings

- Existence of elliptic periodic solutions under periodic perturbations.
- Application of symplectic group analysis to celestial mechanics.
- Results on stability of these periodic solutions.

## Abstract

The existence of elliptic periodic solutions of a perturbed Kepler problem is proved. The equations are in the plane and the perturbation depends periodically on time. The proof is based on a local description of the symplectic group in two degrees of freedom.