A new dynamical indicator for chaos detection in galactic Hamiltonian systems

TL;DR

The paper introduces the f-indicator, a new dynamical parameter for efficiently distinguishing between regular and chaotic motion in galactic Hamiltonian systems, validated against established methods.

Contribution

It presents the f-indicator, a novel, fast, and reliable method for chaos detection in galactic Hamiltonian systems, applicable to both global and local potentials.

Findings

The f-indicator accurately identifies chaos in 2D and 3D systems.

It provides results comparable to Lyapunov exponents and S(c) spectrum.

The method is computationally efficient and reliable.

Abstract

A new dynamical parameter, the f-indicator, is introduced and used in order to distinguish between regular and chaotic motion in galactic Hamiltonian systems. Two kinds of galactic potentials are used: (i) a global potential, which describes the whole galaxy and (ii) a local potential, which is made up of perturbed harmonic oscillators and describes motion near an equilibrium point. The new indicator is based on the energies of the separable system along the x, y and z axis. Comparison between the outcomes obtained using the new dynamical parameter and other methods, such as the maximum Lyapunov Characteristic Exponent (L.C.E), or the S(c) dynamical spectrum, shows that the new dynamical indicator gives fast and reliable results concerning the regular or chaotic character of the orbits. The new indicator was tested in several Hamiltonian systems of two (2D) degrees and three (3D) degrees of freedom.