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

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.