Simple Instability in a 3D Autonomous Hamiltonian system of galactic type

Abstract

In this paper we study the orbital behavior in the neighborhood of simple unstable periodic orbits in a 3D rotating galactic potential. We use the method of color and rotation to visualize the 4D spaces of section. We found four types of structures in the 4D space of section that correspond to four types of orbits. The first three types are sticky chaotic orbits and in the last one the orbit visits all available phase space.