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In this work we propose a new numerical approach to distinguish betweenregular and chaotic orbits in Hamiltonian systems, based on the simultaneousintegration of both the orbit and the deviation vectors using a symplecticscheme, hereby called {\em global symplectic integrator}. In particular, theproposed method allows us to recover the correct orbits character with verylarge integration time steps, small energy losses and short CPU times. Toillustrate the numerical performances of the global symplectic integrator wewill apply it to two well-known and widely studied problems: the H\'enon-Heilesmodel and the restricted three-body problem.

Symplectic integration of deviation vectors and chaos determination.  Application to the H\'enon-Heiles model and to the restricted three-body  problem