Testing the FLI in the region of the Pallas asteroid family

Abstract

Computation of the fast Lyapunov indicator (FLI) is one of the most efficient numerical ways to characterize dynamical nature of motion and to detect phase-space structures in a large variety of dynamical models. Despite its effectiveness, FLI was mainly used for symplectic maps or simple Hamiltonians, but it has never been used to study dynamics of asteroids to a greater extent. This research shows that FLI could also be successfully applied to real (Solar system) dynamics. For this purpose, we focus on the main belt region where the Pallas asteroid family is located. By using the full Solar system model, different sets of initial conditions and different integration times, we managed not only to visualize a large multiplet of resonances located in the region, but also their structures, chaotic boundaries, stability islands therein and the positions of their mutual interaction. In the end, we have identified some of the most dominant resonances present in the region and established a link between these resonances and chaotic areas visible in our maps. We have illustrated that FLI once again has shown its efficiency to detect dynamical structures in the main belt, e.g. in the Pallas asteroid family, with a surprisingly good clarity.