# A family of integrable perturbed Kepler systems

## TL;DR

This paper introduces a family of perturbed Kepler systems within Poisson geometry, demonstrating their integrability via quadratures and providing explicit solutions using Jacobi elliptic functions for specific cases.

## Contribution

It presents a new class of integrable perturbed Kepler systems analyzed through Poisson geometry, with explicit solutions for certain subcases.

## Key findings

- Hamilton equations are integrable by quadratures.
- Explicit solutions are expressed with Jacobi elliptic functions.
- The systems extend classical Kepler problems within a geometric framework.

## Abstract

In the framework of the Poisson geometry of twistor space we consider a family of perturbed 3-dimensional Kepler systems. We show that Hamilton equations of this systems are integrated by quadratures. Their solutions for some subcases are given explicitly in terms of Jacobi elliptic functions.