On the dynamics of Armbruster Guckenheimer Kim galactic potential in a rotating reference frame

Abstract

In this article, we are interested in studying some dynamics aspects for the Armbruster Guckenheimer Kim galactic potential in a rotating reference frame. We introduce a non-integrability condition for this problem using Painlevé analysis. The equilibrium positions are given and their stability is studied. Furthermore, we prove the force resulting from the rotation of the reference frame can be used to stabilize the unstable maximum equilibrium positions. The periodic solutions near the equilibrium positions are constructed by applying Lyapunov method. The permitted region of motion is determined.