Painlev\'e analysis and integrability of three-dimensional Armbruster Guckenheimer Kim galactic potential

TL;DR

This paper uses Painlevé analysis to study the integrability of a 3D galactic potential model, identifying three integrable cases with explicit integrals and exploring their phase space behavior through numerical experiments.

Contribution

It provides a systematic Painlevé analysis of the 3D Armbruster Guckenheimer Kim galactic potential and explicitly derives integrals for three integrable cases.

Findings

Identified three cases of integrability with explicit integrals

Performed numerical experiments revealing chaos-order-chaos phenomena

Enhanced understanding of the phase space structure of the potential

Abstract

The three-dimensional Armbruster Guckenheimer Kim galactic potential in the general form is considered. The integrability of this problem is performed by using the Painlev\'e analysis. We report three cases of integrability, exact integrals of motion are obtained explicitly for each case. A numerical experiment is provided to investigate the classical phase space and explore chaos-order-chaos phenomenon.