On the use of the MEGNO indicator with the Global Symplectic Integrator

TL;DR

This paper demonstrates an efficient method to compute the MEGNO chaos indicator using the Global Symplectic Integrator, emphasizing the importance of integrator choice for analyzing Hamiltonian systems, exemplified through Arnold diffusion.

Contribution

It introduces a joint computation approach for MEGNO with GSI and discusses optimal integrator selection based on Hamiltonian structure.

Findings

Efficient computation of MEGNO with GSI is achieved.

The method's performance is validated on Arnold diffusion.

Integrator choice significantly impacts results.

Abstract

To distinguish between regular and chaotic orbits in Hamiltonian systems, the Global Symplectic Integrator (GSI) has been introduced, based on the symplectic integration of both Hamiltonian equations of motion and variational equations. In the present contribution, we show how to compute efficiently the MEGNO indicator jointly with the GSI. Moreover, we discuss the choice of symplectic integrator, in fact we point out that a particular attention has to be paid to the structure of the Hamiltonian system associated to the variational equations. The performances of our method is illustrated through the study of the Arnold diffusion problem.