Using the S(c) spectrum to distinguish between order and chaos in a 3D galactic potential

TL;DR

This paper introduces the S(c) spectrum as a rapid and effective tool for distinguishing between regular and chaotic orbits in a 3D galactic potential, extending previous 2D analysis.

Contribution

The study develops and applies the S(c) spectrum to 3D galactic potentials, providing a new method for identifying chaos in complex dynamical systems.

Findings

S(c) spectrum successfully distinguishes regular and chaotic orbits.

The method is faster and comparable in accuracy to existing chaos detection techniques.

Application to a barred galaxy model reveals detailed phase space structure.

Abstract

The regular and chaotic character of orbits is investigated in a 3D potential describing motion in the central parts of a barred galaxy. This potential is an extension in the 3D space of a 2D potential based on a family of figure-eight orbits, which was produced using the theory of the inverse problem. Starting from the results obtained from the 2D system, we proceed to locate the regions in the phase space of the 3D potential, producing regular or chaotic orbits. In order to obtain this we use a new dynamical parameter, the S(c) spectrum, which proves to be a useful and fast indicator in order to distinguish regular motion from chaos in 3D potentials. Comparison with other methods for detecting chaos is also discussed.